Question

practice e:

adelle, the sofa cushion snoop, has \\$29.20 in dimes and quarters. if adelle has 100 more quarters than dimes, how many dimes does she have?

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dimes

Explanation:

Define the variables

Let \(d\) represent the number of dimes.
Let \(q\) represent the number of quarters.

Set up the system of equations

Using the given information:

1. The total value is \$29.20. Since a dime is worth \$0.10 and a quarter is worth \$0.25:

$$0.10d + 0.25q = 29.20$$

Multiplying by 100 to clear decimals:

$$10d + 25q = 2920$$

1. There are 100 more quarters than dimes:

$$q = d + 100$$

Substitute and solve for d

Substitute the expression for \(q\) into the value equation:

$$10d + 25(d + 100) = 2920$$

$$10d + 25d + 2500 = 2920$$

$$35d + 2500 = 2920$$

$$35d = 420$$

$$d = 12$$

Answer:

Adelle, the sofa cushion snoop, has \$29.20 in dimes and quarters. If Adelle has 100 more quarters than dimes, how many dimes does she have?
<blank>12</blank> dimes