Question

1. phyllis has 14 coins. all are quarters or dimes. if her coins have a value of $2.30, how many of each does she have?

Explanation:

Step1: Define Variables

Let \( q \) be the number of quarters and \( d \) be the number of dimes.
We know two equations:

1. \( q + d = 14 \) (total number of coins)
2. \( 0.25q + 0.10d = 2.30 \) (total value of coins, in dollars)

Step2: Solve the System of Equations

From the first equation, we can express \( d \) as \( d = 14 - q \).
Substitute \( d = 14 - q \) into the second equation:

$$
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$$

Step3: Find the Number of Dimes

Substitute \( q = 6 \) into \( d = 14 - q \):
\( d = 14 - 6 = 8 \)

Answer:

Phyllis has 6 quarters and 8 dimes.