Question

you need both answers for this one. dante has 27 coins that are all dimes and quarters. the value of the coins is $4.35. how many dimes and how many quarters does dante have? type your answer...

Explanation:

Step1: Define variables

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

Step2: Set up coin count equation

Total coins: $d + q = 27$

Step3: Set up value equation

Total value (in cents): $10d + 25q = 435$

Step4: Solve for one variable

From Step2: $d = 27 - q$

Step5: Substitute into value equation

$10(27 - q) + 25q = 435$
$270 - 10q + 25q = 435$
$15q = 435 - 270$
$15q = 165$
$q = \frac{165}{15} = 11$

Step6: Find number of dimes

$d = 27 - 11 = 16$

Answer:

Dante has 16 dimes and 11 quarters.