Question

1. michael has 27 coins in all, valuing $4.50. if he only has quarters and dimes, how many of each kind does he have?

Explanation:

Step1: Define variables for coins

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

Step2: Set up total coins equation

Total coins: $q + d = 27$ → $d = 27 - q$

Step3: Set up total value equation

Convert values to cents: $25q + 10d = 450$

Step4: Substitute $d$ into value equation

Substitute $d=27-q$: $25q + 10(27 - q) = 450$

Step5: Simplify and solve for $q$

Expand: $25q + 270 - 10q = 450$
Combine terms: $15q + 270 = 450$
Subtract 270: $15q = 180$
Solve: $q = \frac{180}{15} = 12$

Step6: Calculate number of dimes

$d = 27 - 12 = 15$

Answer:

12 quarters and 15 dimes