Question

Kevin and Randy Muise have a jar containing 82 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$12.10. How many of each type of coin do they​ have? The jar contains nothing quarters.

Answer 1

Answer: The jar contains 40 quarters and 42 nickels.

Step-by-step explanation:

The worth of a quarter is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of quarters that they have in the jar.

Let y represent the number of nickels that they have in the jar.

Kevin and Randy Muise have a jar containing 82 ​coins, all of which are either quarters or nickels. This means that

x + y = 82

The total value of the coins in the jar is ​$12.10. This means that

0.25x + 0.05y = 12.1 - - - - - - - - - - - 1

Substituting x = 82 - y into equation 1, it becomes

0.25(82 - y) + 0.05y = 12.1

20.5 - 0.25y + 0.05y = 12.1

- 0.25y + 0.05y = 12.1 - 20.5

- 0.2y = - 8.4

y = - 8.4/ - 0.2

y = 42

x = 82 - y = 82 - 42

x = 40