Question

1. the 80 eighth graders took a trip to washington, dc. the boys numbered 16 fewer than twice the number of girls. how many of the eighth graders are girls?

Explanation:

Step1: Define variables

Let \( g \) be the number of girls and \( b \) be the number of boys. We know that the total number of eighth - graders is 80, so \( g + b=80 \). Also, the boys numbered 16 fewer than twice the number of girls, so \( b = 2g-16 \).

Step2: Substitute and solve

Substitute \( b = 2g - 16 \) into the equation \( g + b=80 \). We get \( g+(2g - 16)=80 \).
First, simplify the left - hand side: \( g + 2g-16=80 \), which is \( 3g-16 = 80 \).
Then, add 16 to both sides of the equation: \( 3g-16 + 16=80 + 16 \), so \( 3g=96 \).
Next, divide both sides by 3: \( g=\frac{96}{3}=32 \).

Answer:

The number of girls among the eighth - graders is 32.