Question

1. amerigo has 18 more quarters than dimes in his coin collection. the total amount of money he has is $15.70. how many dimes does he have? he has 32 dimes. he has 28 dimes. he has 50 dimes.

Explanation:

Step1: Define Variables

Let \( d \) be the number of dimes. Then the number of quarters is \( d + 18 \).

Step2: Write Value Equations

The value of dimes is \( 0.10d \) dollars, and the value of quarters is \( 0.25(d + 18) \) dollars. The total value is \( 15.70 \) dollars, so:

$$ 0.10d + 0.25(d + 18) = 15.70 $$

Step3: Solve the Equation

First, expand the equation:

$$ 0.10d + 0.25d + 4.5 = 15.70 $$

Combine like terms:

$$ 0.35d + 4.5 = 15.70 $$

Subtract \( 4.5 \) from both sides:

$$ 0.35d = 15.70 - 4.5 = 11.20 $$

Divide both sides by \( 0.35 \):

$$ d = \frac{11.20}{0.35} = 32 $$

Answer:

He has 32 dimes.