Question

1. gina has five times as many dimes as quarters. the total value of the dimes and quarters is $4.50. find how many dimes gina has.

Explanation:

Step1: Define variables

Let $q$ = number of quarters, $d = 5q$ (number of dimes, since dimes are 5× quarters)

Step2: Set up value equation

Value of quarters: $0.25q$, Value of dimes: $0.10d = 0.10(5q)$. Total value:
$$0.25q + 0.10(5q) = 4.50$$

Step3: Simplify and solve for q

Simplify the left side:
$$0.25q + 0.50q = 4.50$$
$$0.75q = 4.50$$
Solve for $q$:
$$q = \frac{4.50}{0.75} = 6$$

Step4: Calculate number of dimes

Substitute $q=6$ into $d=5q$:
$$d = 5 \times 6 = 30$$

Answer:

30