The kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.
What is a polynomial equation?A polynomial equation is a sum of constants and variables. A polynomial is an expression consisting of indeterminate's (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
For the given situation,
The equation [tex]f(x) = x^3 - x^2 - x + 1[/tex]
The roots of the polynomial equation can be found as follows,
Step 1:
Substitute the value of x in which the equation f(x) equals zero.
⇒ Put [tex]x = 1[/tex], the equation becomes
⇒ [tex]f(1) = 1^3 - 1^2 - 1 + 1[/tex]
⇒ [tex]f(1) = 0[/tex]
Thus [tex](x - 1)[/tex] is the one root of the equation.
Step 2:
The other roots can be found by framing the quadratic equation on dividing the equation [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex]
On dividing [tex]f(x) = x^3 - x^2 - x + 1[/tex] by [tex](x - 1)[/tex] we get the quotient,
⇒ [tex](x^{2} -1)[/tex]
Step 3:
Now factorize the quadratic equation, [tex](x^{2} -1)[/tex]
It can be expand using the identity,
⇒ [tex](x^{2} -1^{2} ) = (x+1)(x-1)[/tex] [∵ (a^2 - b^2) = (a+b)(a-b) ]
Thus the factors of the equation are [tex](x-1)(x+1)(x-1)[/tex]. So the roots are [tex]1,-1,1[/tex].
Hence we can conclude that the kind of roots does the equation f(x) is option (C) 3 real roots is the correct answer.
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Talia spent \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of this week's allowance on candy. Of the money she spent on candy, \dfrac56 6 5 start fraction, 5, divided by, 6, end fraction was spent on gummy bears.
Answer:
15/24
Step-by-step explanation:
Talia spent 3/4 of this week's allowance on candy. Of the money she spent on candy, 5/6 was spent on gummy bears.
What fraction of this week's allowance did Talia spend on gummy bears?
Answer: Let this weeks allowance be x. Talia spent 3/4 of the weeks allowance on candy, therefore the money spent on candy = (3/4)x.
Out of the money spent on candy, 5/6 was spent on gummy bears. Therefore the money spent on gummy bears = 5/6 × (3/4)x = (15/24)x.
This means that the fraction of money spent on gummy bears was 15/24 of the weeks allowance.
ASAP i need to know the complete working
Answer:
a(1):30%
(2):2135.34
(3):15000
Step-by-step explanation:
a(1):the total is 18750 and 5625 was not taxed therefore 5625 of 18750 was not taxed so get the amount expressed as a percentage by multiplying by 100
{5625/18750}×100
(2):so get the tax from the taxable amount and the taxable amount is 13125 and the tax is 22% of it so (22/100)×13125=2887.5
she takes home the amount remaining after taxation so 18750-2887.5(tax)(don't subtract 5625)=15862.5
she receives the above amount in 52 equal amounts so divide 15862.5/52 to get one amount =305.048 (meaning that per week she receives one of the 52 equal amounts I guess)
(3):so the original salary before moving to A was 100% but after moving it increases by 25 so the salary is 125% =18750(don't deduct tax I guess) so it will be (100/125)×18750
20 POINTS! Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+10x−1 B. f(x)=−3x2+4x−1 C. f(x)=−2x2+5x−1 D. f(x)=−5x2+8x−1 3) Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13). A. y=−3(x−3)2+5 B. y=2(x−3)2+5 C. y=−2(x−3)2+5 D. y=2(x+3)2−5
Answer:
1) f(x) = 4·x² - 3·x + 6
2) f(x) = -2·x² + 5·x - 1
3) y = 2·(x - 3)² + 5
Step-by-step explanation:
1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows
The general form of a quadratic function is f(x) = a·x² + b·x + c
Where, in (x, y), f(x) = y, and x = x
Therefore for the point (0, 6), we have;
6 = 0·x² + 0·x + c
c = 6
We have c = 6
For the point (2, 16), we have;
16 = a·2² + b·2 + 6
10 = 4·a + 2·b.............................(1)
For the point (3, 33), we have;
33 = a·3² + b·3 + 6
27 = 9·a + 3·b............................(2)
Multiply equation (1) by 1.5 and subtract it from equation (2), we have;
1.5 × (10 = 4·a + 2·b)
15 = 6·a + 3·b
27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;
27 - 15 = 9·a - 6·a+ 3·b - 3·b
12 = 3·a
a = 12/3 = 4
a = 4
From equation (1), we have;
10 = 4·a + 2·b = 4×4 + 2·b
10 - 4×4 = 2·b
10 - 16 = 2·b
-6 = 2·b
b = -3
The function, f(x) = 4·x² - 3·x + 6
2) Where the points are (-1, -8), (0, -1), (1, 2), we have;
For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)
For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)
For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)
Adding equation (1) to equation (3) gives
-8 + 2 = a - b + c + a + b + c = 2·a + 2·c where, c = -1, we have
-8 + 2 = -6 = 2·a + 2
2·a = -6 + 2 = - 4
a = -8/2 = -2
From equation (3), we have;
2 = a + b + c
b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5
f(x) = -2·x² + 5·x - 1
3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola
The vertex equation of a parabola is y = a(x - h)² + k
Where;
(h, k) = Vertex (3, 5)
(x, y) = (1, 13)
We have
13 = a·(1 - 3)² + 5
13 = a·(-2)² + 5
13 - 5 = a·(-2)² = 4·a
4·a = 8
a = 8/4 = 2
The equation is y = 2·(x - 3)² + 5.
Simplify the expression. (5x2 - x - 7) + (2x2 + 3x + 4)
Answer:11+2x
Step-by-step explanation:
(10-7-x)+(4+4+3x)
3-x+8+3x
3+8+3x-x
11+2x
SUPER URGENT HELP NEEDED! BRAINLIEST AVAILABLE!
HELP IN NEED THESE ANSWERED ASAP! WILL GIVE BRAINLIEST TO THE PERSON WHO CAN ANSWER THESE QUICKEST AND I NEED ANSWERS TO ALL 4, BUT DON'T NEED ANY WORKING OUT, BUT IF YOU WANT TO YOU CAN! ALSO IF YOU ONLY KNOW THE ANSWER TO 1 OR 2 OF THEM, JUST SEND THAT, AND I WILL STILL GIVE YOU BRAINLIEST!
Answer:
1B)[tex] 11[/tex]
1C)$ 5104$
1D) $A=3 B=-51$
1E) [tex] \frac{1}{8}[/tex]
Step-by-step explanation:
The above answer!
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?
nCr(20, 2) = 190 ways of selecting 2 from 20
nCr(10, 1) = 10 ways of selecting 1 from 10
To find the over all probability of winning,
Calculate the Harmonic Mean (19) and divide by 2
Equivalent to
1/ (1//190 + 1/10) =9.5
So the probability is 1/9.5 = 2/19.
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t
Answer:
3.2t-2.4Step-by-step explanation:
[tex]\\-3.6-1.9t+1.2+5.1t\\\mathrm{Group\:like\:terms}\\\\=-1.9t+5.1t-3.6+1.2\\\\\mathrm{Add\:similar\:elements:}\:-1.9t+5.1t=3.2t\\\\=3.2t-3.6+1.2\\\\=3.2t-2.4[/tex]
Answer:
3.2t -2.4
Step-by-step explanation:
-3.6-1.9t+1.2+5.1t
Like by terms = -1.9t+5.1t - 3.6 +1.2
Solve left to right step 1 = 3.2t - 3.6 +1.2
Solve step 2 = 3.2t - 2.4
HELLP BRAINLIEST!!! Could someone clarify something for me?? What is the expression that represents the area of the rectangle? Do i solve this or do i just find the expression? Also could you help me solve the problem below?
Answer:
See below.
Step-by-step explanation:
The question doesn't ask you to find the area, it just ask for the expression that represents the area.
The area of rectangle is A=bh, where b and h are each of the side lengths.
Since we know the sides are (2x+7) and (5x+9), this means that the expression for the area of the rectangle is:
[tex](2x+7)(5x+9)[/tex]
To find the degree and classification, expand the factors:
[tex]=(2x+7)(5x+9)\\=(10x^2+18x+35x+63)\\=10x^2+53x+63[/tex]
Thus, this is a second degree quadratic expression
And from Part A, when we multiplied (2x+7)(5x+9), we got another polynomial (10x^2+52x+63). Thus, this rerepresents the closure property of polynomials, where multiplying a polynomial by another gets another polynomial.
.
Answer:
see below
Step-by-step explanation:
Part A
(2x+7) ( 5x+9)
Foil
first 2x*5x = 10x^2
outer: 2x*9 = 18x
inner: 7*5x= 35x
last: 7*9 = 63
Add together
10x^2 +18x+35x+63
10x^2+53x+63
Part B
This is a second degree polynomial called a quadratic
Part C
When we multiply two polynomials together, we get another polynomial. This is the closure property for multiplication of polynomials
is this right? someone please check?
Answer:
The answer looks correct.
Step-by-step explanation:
All the other option doesn't match the above question's statement.
The last answer is the correct (in my opinion)
Answer:
Absolutely Correct
Step-by-step explanation:
Based on the definition of midpoint;
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
meaning the distance from the midpoint to one end is the same as the distance to the other end
show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x
Answer:
see explanation
Step-by-step explanation:
Given
(2x + 3)³
= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL
= (2x + 3)( 4x² + 12x + 9)
= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis
= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms
= 8x³ + 36x² + 54x + 27
Choose all properties that were used to simplify the following problem:
(38 +677) + (-38)
[677 + 38) + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The properties 1‚ 2‚ 4‚ and 5. are used
The properties used to simplify problem are 1 , 2 and 4.
A problem which is simplified is given ; (38 +677) + (-38).
What are the correct options ?
How will you represent the associative properties of addition ?
Associative properties are represented by ; (A + B ) + C = A + ( B + C ).
As per the data given in question ;
Let's check which options are suitable.
( 38 + 677 ) + ( -38 ) = 38 + ( 677 - 38 )
(A + B ) + C = A + ( B + C )
So , this is the associative property.
677 + 0 = 677
A + 0 = A
So , this is the additive identity.
677 + [38 + (-38)]
Here ; 38 + ( -38 ) represents ;
A + (-A) = 0.
So , this is the additive inverse.
Thus , the properties used to simplify problem are 1 , 2 and 4.
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Evaluate 5(14 - 2³) +8 ÷ 2.? Plz help me, will mark you as brainliest A. 26 B. 34 C. 44 D. 56
Answer:
[tex]\large \boxed{\sf B. \ 34}[/tex]
Step-by-step explanation:
[tex]5(14 - 2^3 ) +8 \div 2[/tex]
[tex]\sf Solve \ brackets.[/tex]
[tex]2^3 =8[/tex]
[tex]5(14 - 8 ) +8 \div 2[/tex]
[tex]14-8=6[/tex]
[tex]5(6 ) +8 \div 2[/tex]
[tex]\sf Multiply \ and \ divide.[/tex]
[tex]5(6)=30[/tex]
[tex]8 \div 2 = 4[/tex]
[tex]30 +4[/tex]
[tex]\sf Add.[/tex]
[tex]34[/tex]
Answer: 34
Step-by-step explanation: It's very easy to make mistakes in order of operations problems if you try to do too much of the problem in your head.
It really is worth the extra time it takes to write out every step.
P E M D A S
Parenthses
Exponents
Multiplication/Division
Addition/Subtraction
In this problem, simplify (14 - 2³) first
because it's located inside the parenthses.
2³ is 8 so our second step reads 5(14 - 8) + 8 ÷ 2.
14 - 8 is 6 so we have 5(6) + 8 ÷ 2.
Now multiplication and division are based on order of appearance.
Since multiplication comes first, we do it first.
5(6) is 30 so we have 30 + 8 ÷ 2.
Now we can do the division.
8 ÷ 2 is 4 and we have 30 + 4 which is 34.
Can anyone help me with this question ?
Answer:
each shirt costs $17.50.
Step-by-step explanation:
we have the equation 4(12.50) + 4(2x) = 190
because each friend (4 total friends) get one hat and two shirts.
we simplify the equation to 50 + 8x = 190
subtract 50 from both sides
8x = 140
divide both sides by 8
x = 17.5
therefore, each shirt costs $17.50.
Pattern A starts at 20 and has the rule 'subtract 2 Pattern B starts at 20 and has
the rule 'subtract I". Which shows the first several terms of Patterns A and B?
Pattern A: 20, 17, 15, 13, 11,
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 21, 22, 23, 24, 25
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 22, 24, 26, 28, 30
Pattern B: 20, 21, 22, 23, 24, 25
Answer:
The correct option is C.
Step-by-step explanation:
The two patterns are defined as follows:
Pattern A starts at 20 and has the rule 'subtract 2'.Pattern B starts at 20 and has the rule 'subtract 1'.Form the two patterns as follows:
Pattern A : 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0
Pattern B : 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
The first several terms of Patterns A and B are shown by:
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 19, 18, 17, 16, 15
Thus, the correct option is C.
PlZ HELP NOW ASAP!!!
Answer:
x=33
Step-by-step explanation:
x for ?
sinx=opposite/hypotenuse
sinx=162.5/298=0.54530201
convert to degrees using arcsin(0.54530201)= 33.043
33 degrees rounded to the nearest ones
ANSWER QUICKLY PLZZZZZZ
ANSWER QUESTION C
Answer:
[tex] \boxed{12}[/tex]Step-by-step explanation:
E is 5 more than d
f is 7 less than d
a) e = d + 5
b) f = d - 7
c) plug the values of e and f
[tex] = d + 5 - (d - 7)[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = d + 5 - d + 7[/tex]
Since, two opposites add up to zero , remove them from the expression
[tex] = 5 + 7[/tex]
Add the numbers
[tex] = 12[/tex]
Hope I helped!
Best regards!
Solve for x: 3x-4=2x-10
Answer:
x = - 6
Step-by-step explanation:
3x - 4 = 2x - 10
3x -2x = 4 - 10
x = - 6
For the equation 3x-4=2x-10, the value of x is -6.
The given equation is 3x-4=2x-10.
x is the variable in the equation.
Plus and minus are operators.
To solve for x, subtract 2x from both sides:
3x-2x-4=2x-2x-10
x-4=-10
Add 4 on both sides:
x=-10+4
x=-6
Hence, the value of x is -6.
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A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Evaluate 6 · 3 ÷ √9 - 1. plz help, will mark brainliest A. 2 B. 3 C. 5 D. 6
Answer: C. 5
Step-by-step explanation:
[tex]6 \cdot3\div \sqrt{9}-1[/tex]
[tex]6 \cdot 3=18[/tex]
[tex]\sqrt{9}=3[/tex]
[tex]18\div \:3-1[/tex]
[tex]18\div \:3=6[/tex]
[tex]6-1[/tex]
[tex]=5\\[/tex]
The value is 16.
What is square root?The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents. Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 3^2. Here, the exponent is 2, and we call it a square.
We can use four methods to find the square root of numbers and those methods are as follows:
Repeated Subtraction Method of Square RootSquare Root by Prime Factorization MethodSquare Root by Estimation MethodSquare Root by Long Division MethodGiven:
6 · 3 ÷ √9 - 1
6*3 = 18
√9 - 1 = 3-1 = 2
So,
6 · 3 ÷ √9 - 1
=18- 2
=16
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Water flows through a pipe at a rate of 4 quarts per day. Express this rate of flow in liters per week. Round your answer to the nearest tenth.
Answer:
26.5 liters
Step-by-step explanation:
We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78 by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.
Beverly made a deposit of 375 into our checking account. Then she
withdraw $65. The next day, she wrote a check for $135. She had 475 before any of these transactions how much money is in her account now?
Answer:
650
Step-by-step explanation:
475+375-65-135=650
pls i want help in this sum
Step-by-step explanation: The first rectangle to the right is 24 because 10+14 equals 24. The rectangle to the left is 19 because 10+9 equals 19. Finally the rectangle on the bottom is 23 because 14+9 is 23
a number is multiplied by 5 and the results is twice the number added to 2 find the number
Answer:
5x=2x+2
3x=2
X=2/3
Hope this helps ФωФ
Solve for xxx. 12x+7 4012x+7 40
Answer:
[tex]x = 2.75[/tex]
Step-by-step explanation:
I'm assuming you have an equation
[tex]12x + 7 = 40\\[/tex]
and you want to solve for x.
This is easy. First, subtract 7 from each side of the equation.
[tex]12x+7-7 = 40-7[/tex]
[tex]12x = 33[/tex]
Then divide both sides by 12, to get x alone on the left side.
[tex]\frac{12x}{12} = \frac{33}{12}[/tex]
[tex]x = \frac{33}{12} = 2.75[/tex]
if one square yard of carpet costs $15.40, how much will 45.5 square yards cost? ( value only, no commas, dollar signs, symbols, or units)
Work Shown:
1 square yard = 15.40 dollars
45.5*1 square yard = 45.5*15.40 dollars
45.5 square yards = 700.70 dollars
In the second step, I multiplied both sides by 45.5 to turn the "1 square yard" into "45.5" square yards.
The number that is 75% of one less than a number n.
Answer:
The number is n-0.75
Step-by-step explanation:
Here in this question, we are interested in giving a number which is 75% of 1 less than a number n.
The first thing we do here is to calculate the value of 75% of 1.
That would be;
75/100 * 1 = 0.75
So this value less than n will be;
n- 0.75
an inch worm is how long in general
Answer:
A inch
Step-by-step explanation:
Simplify. Can you explain it also?
[tex] \frac{9 {c}^{3} {de}^{2} }{12 {c}^{2}d {e}^{3} }[/tex]
Answer:
The answer is
[tex] \frac{3c}{4e}[/tex]Step-by-step explanation:
[tex] \frac{9 {c}^{3}d {e}^{2} }{12 {c}^{2} d {e}^{3} } [/tex]To solve the fraction reduce the fraction with d
That's we have
[tex] \frac{9 {c}^{3} {e}^{2} }{12 {c}^{2} {e}^{3} } [/tex]Next simplify the expression using the rules of indices to simplify the letters in the fraction
For c
Since they are dividing we subtract the exponents
We have
[tex] {c}^{3} \div {c}^{2} = {c}^{3 - 2} = c^{1} = c[/tex]For e
[tex]e^{2} \div {e}^{3} = e^{2 - 3} = {e}^{ - 1} = \frac{1}{e} [/tex]Substituting them into the expression we have
[tex] \frac{9c}{12e} [/tex]Reduce the fraction by 3
We have the final answer as
[tex] \frac{3c}{4e} [/tex]Hope this helps you
1. An atom consist of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of -1.Remember number of electrons is equal to number of protons, while answering these questions i) What is the charge on an atom? Ii) What will be the charge of an atom if it loses an electron? Iii) What will be the charge of an atom if it gains an electron?
Answer:
I) no charge
ii) it will be positively charged
iiI) it will be negatively charged
Step-by-step explanation:
An atom is composed of electrons, neutrons and protons. Electrons are negatively charged while protons are positively charged. The number of electrons and protons in a neutral atom are exactly the same. This ensures the electrical neutrality of the atom.
However, if an atom looses an electron, there are now more protons than electrons present in the atom hence the atom is positively charged.
Similarly, if an atom gains an electron, it now contains more electrons than protons, hence it is negatively charged.
A grocery sold 5kg of wheat flour at Rs30 per kg and gained 20%. If he had sold it at Rs27 per kg, what would be his gain or loss percent.
Answer:
His gain percent would have been 8%
Step-by-step explanation:
The key to answering this question is to first calculate the price at which the wheat flour was bought.
Mathematically;
% profit = (selling price-cost price)/cost price * 100%
Let the cost price be $x
Thus;
% profit = (30-x)/x * 100
20 = 100(30-x)/x
20x = 3000-100x
100x + 20x = 3000
120x = 3000
x = 3000/120
x = Rs 25
So let’s assume he sold at Rs 27
His profit would have been 27-25 = 2
His gain or loss percentage would’ve been;
2/25 * 100/1 = 200/25 = 8% (gain, since selling price is greater than the cost price)
