Question

solving mixture problems
alex has 84 quarters and nickels worth a total of $17.80.
which equation can be used to find q, the number of quarters alex has?
0.05(84 - q) + 0.25q = 17.80
0.25(q - 84) + 0.05q = 17.80
0.25q + 0.05(q - 84) = 17.80
0.05q + 0.25(84 - q) = 17.80

Explanation:

Step1: Define variables

Let \( q \) be the number of quarters. Since there are a total of 84 coins (quarters and nickels), the number of nickels is \( 84 - q \).

Step2: Determine value of each type

The value of a quarter is \( \$0.25 \), so the total value of quarters is \( 0.25q \). The value of a nickel is \( \$0.05 \), so the total value of nickels is \( 0.05(84 - q) \).

Step3: Set up the equation

The total value of quarters and nickels is \( \$17.80 \). So, the equation is the sum of the value of quarters and the value of nickels equals \( 17.80 \), which is \( 0.25q + 0.05(84 - q)=17.80 \).

Answer:

\( 0.25q + 0.05(84 - q) = 17.80 \) (the third option among the given equations)