How many of each coin are in the vending machine

Question

A vending machine only accepts dimes and quarters. There are 85 coins in the machine with a total value of $16.75. How many of each coin are in the machine.

Answer 1

Let x be the number of dimes

Since there are 85 total coins, the total number of quarters MUST be 85 - x

 

The total value of all the dimes is .10 multiplied by x = .10x.

The total value of all the quarters is .25 multiplied by 85 - x = .25(85 - x)  <--- Must have parentheses!

 

The total value of all the coins is .10x + .25(85 - x)

 

Set this total value equal to the total value given and solve for x

.10x + .25(85 - x) = 16.75

 

.10x + .25(85 - x) = 16.75

.10x + 21.25 - .25x = 16.75

-.15x + 21.25 = 16.75

-.15x = -4.5

   x = 30

Therefore there are 30 dimes and 55 quarters.