Question

Jada had some dimes and quarters that had a total value of $12.50. The relationship between the number of dimes, d, and the number of quarters, q, can be expressed by the equation

0.1d + 0.25q = 12.5.
If Jada has 10 quarters, how many dimes does she have?

Answer 1

Given the expression

`0.1\cdot d+0.25\cdot q=12.5`

Where

d = number of dimes

q = number of quarters

Given that there are 10 quarters, find the number of dimes.

To find it, substitute q by 10.

`\begin{gathered} 0.1\cdot d+0.25\cdot10=12.5 \\ 0.1\cdot d+2.5=12.5 \end{gathered}`

To isolate d, subtract 2.5 from each side:

`\begin{gathered} 0.1\cdot d+2.5-2.5-12.5-2.5 \\ 0.1d=10 \end{gathered}`

Finally, divide both sides by 0.1:

`\begin{gathered} (0.1\cdot d)/(0.1)=(10)/(0.1) \\ d=10\cdot10 \\ d=100 \end{gathered}`

Answer: There are 100 dimes.