You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces in multiples of four, and to buy four, you need $0.23. He only allows you to do this by using 3 pennies and 2 dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have 636.3 g of pennies, and each penny weighs 3.03 g. Each dime weighs 2.29 g. Each piece of candy weighs 10.23 g.


Required:

a. How many pennies do you have?

b. How many dimes do you need to buy as much candy as possible?

c. How much should all these dimes weigh?

d. How many pieces of candy could you buy? (number of dimes from part b)

e. How much would this candy weigh?

f. How many pieces of candy could you buy with twice as many dimes?

a. We have 210 pennies

b. We need 140 dimes to buy as much candy as possible.  

c. All these dimes should weigh 320.6 g.

d. We can buy 70 pieces of candy.

e. The total weight of the candies will be 2864.4 g

f. Using 3 pennies and 2 dimes as a pack to buy candies we can not buy more pieces of candy because we would need more pennies.    

a. To find the number of pennies we need to divide the total mass of pennies ([tex]m_{t_{p}}[/tex]) by the mass of each one of them ([tex]m_{p}[/tex]):

[tex] N = \frac{m_{t_{p}}}{m_{p}} = \frac{636.3 g}{3.03 g} = 210 [/tex]

Hence, we have 210 pennies.  

b. We can find the total number of pieces in multiples of four that we can buy with 210 pennies. To buy one piece we need to use 3 pennies and 2 dimes, so the number of total pieces is:

[tex] 3P = 210 [/tex]

Where P is for pennies

[tex] P = \frac{210}{3} = 70 [/tex]

Hence, we can buy a total of 70 pieces in multiples of four candies.

Now, from this total of 70 pieces, we can use the following number of dimes:

[tex] 2D = 70 [/tex]

Where D is for dimes      

[tex] D = \frac{70}{2} = 140 [/tex]

Therefore, we need 140 dimes to buy as much candy as possible.

c. The mass of the total amount of dimes ([tex] m_{t_{d}}[/tex]) is:

[tex] m_{t_{d}} = 140*2.29 g = 320.6 g [/tex]

Hence, all these dimes should weigh 320.6 g.

d. We know that we can buy a total of 70 pieces in multiples of four candies (calculated above).

Then, we can buy 70 pieces of candy.

e. Knowing that each piece is a multiple of 4 candies, the weight of the 70 pieces of candy ([tex]m_{c}[/tex]) is:

[tex] m_{c} = 70*4*10.23 g = 2864.4 g [/tex]      

f. Since we can buy pieces in multiple of four candies using 3 pennies and 2 dimes if we have now twice as many dimes, we can not buy more pieces of candy because we would need more pennies.      

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I hope it helps you!                                              

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