Question

12. In anticipation of going on vacation, you have been saving the dimes and nickels of your small change for the past year to have a little extra spending money. When you bring the change to a coin counter, your receipt shows that you have 906 coins for a total of $64.10.Let x represent the number of dimes you have, and y represent the number of nickels you have.a. Write an equation to represent the number of coins that you have (3 points)b. Write an equation to represent how much money you have.(3 points)c. Solve the system of equations to find out how many dimes and how many nickels you have.(6 points)

Answer 1

x: number of dimes

y: number of nickels

a. you have 906 coins, then:

x + y = 906

b. you have a total of $64.10, then:

0.1x + 0.05y = 64.10

c. Isolating y from the first equation,

y = 906 - x

Substituting this result into the second equation and solving for x,

0.1x + 0.05(906 - x) = 64.10

0.1x + 0.05*906 - 0.05x = 64.10

0.05x + 45.3 = 64.1

0.05x = 64.1 - 45.3

x = 18.8/0.05

x = 376

And

y = 906 - 376

y = 530

You have 376 dimes and 530 nickels