Questions: You have 3.70 in dimes and quarters. You have 5 more quarters than dimes. How many of each type of coin do you have?

Transcript text: You have $3.70 in dimes and quarters. You have 5 more quarters than dimes. How many of each type of coin do you have?

Solution

Solution Steps

Step 1: Define Variables

Let $ d $ represent the number of dimes and $ q $ represent the number of quarters.

Step 2: Set Up Equations

From the problem, we have two key pieces of information:

The total value of the coins is $3.70, which can be expressed as: \[ 0.10d + 0.25q = 3.70 \]
There are 5 more quarters than dimes, which can be expressed as: \[ q = d + 5 \]

Step 3: Substitute and Simplify

Substitute the expression for $ q $ from the second equation into the first equation: \[ 0.10d + 0.25(d + 5) = 3.70 \] Simplify the equation: \[ 0.10d + 0.25d + 1.25 = 3.70 \] Combine like terms: \[ 0.35d + 1.25 = 3.70 \] Subtract 1.25 from both sides: \[ 0.35d = 2.45 \] Divide by 0.35: \[ d = 7 \]

Step 4: Solve for the Number of Quarters

Use the value of $ d $ to find $ q $: \[ q = d + 5 = 7 + 5 = 12 \]