i have 30 coins. some of them are dimes, and some of them are quarters. in total, i have $4.05. how many of each coin do i have?

Answers

Answer 1

Answer: 23 dimes & 7 quarters

Step-by-step explanation:

Dimes = 10¢ = $0.10Quarters = 25¢ = $0.25Number of dimes = xNumber of quarters = y

You can create two equations:

[tex]\left \{ {{x + y = 30} \atop {0.10x + 0.25y =4.05}} \right.[/tex]

Rearrange x + y = 30:

[tex]y=30-x[/tex]

Substitute it into the x-value of the other equation & solve:

[tex]0.10x + 0.25y =0.10x + 0.25(30-x)=4.05\\0.10x+7.5-0.25x=4.05\\0.10x-0.25x=4.05-7.5\\-0.15x=-3.45\\x=\frac{-3.45}{-0.15} =23[/tex]

With the x-value, substitute it back to the original equation to find y-value:

[tex]y=30-x=30-23=7[/tex]

Therefore, there are 23 dimes & 7 quarters.

Answer 2

There are 23 dimes and 7 quarters.

Given that, the total number of coins=30.

How to convert dimes to dollars?

To convert dimes to dollars we need to multiply the number of dimes by 0.1.

Let the number of dimes be x, and then the number of quarters will be 30-x.

Now, x×0.1+(30-x)×0.25=4.05

⇒-0.15x=-3.45

⇒x=23

30-x=7

Hence, there are 23 dimes and 7 quarters.

To learn more about equations visit:

https://brainly.com/question/2263981.

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