Question

A jar is filled with only dimes and quarters. The jar contains a total of 60 coins and the value of the jar is $11.25. How many quarters are in the jar?

Answer 1

35 quarters

Explanation:

This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

• 
  `d+q=60` is an equation representing the total number of coins
• 
  `0.10d+0.25q=11.25` is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get
`d=60-q`. We now substitute this for d in the second equation.

`0.10(60-q)+0.25q=11.25\\6-0.10q+0.25q=11.25\\6+0.15q=11.25`

After simplifying, we subtract 6 across and divide by the coefficient of q.

`6+0.15q=11.25\\0.15q=5.25\\q=35`

We now know of the 60 coins that 35 are quarters. To find the total value of the quarters, we multiply 35 by 0.25 and find 8.75.