Question

justin has $3.25 worth of dimes and quarters. he has a total of 16 dimes and quarters altogether. determine the number of dimes and the number of quarters that justin has.
answer
there are

dimes and

quarters.

Explanation:

Step1: Define variables

Let $d$ = number of dimes, $q$ = number of quarters.

Step2: Set up total count equation

$d + q = 16$

Step3: Set up total value equation

Convert dollars to cents: $10d + 25q = 325$

Step4: Solve for $d$ from Step2

$d = 16 - q$

Step5: Substitute into value equation

$10(16 - q) + 25q = 325$
$160 - 10q + 25q = 325$
$15q = 325 - 160$
$15q = 165$
$q = \frac{165}{15} = 11$

Step6: Find $d$ using $q=11$

$d = 16 - 11 = 5$

Answer:

There are 5 dimes and 11 quarters.