the ratio of men to women at a basketball game was 3:2 suppose there were 90 men at the basketball game

Question

how many women were at the game? justify your answer

Answer 1

To determine how many women were at the basketball game, we can use the given ratio of men to women, which is 3:2.

1. Let's denote the number of men as \( M \) and the number of women as \( W \).

2. According to the ratio, we can express this as: \[ \frac{M}{W} = \frac{3}{2} \]

3. We know that there were 90 men at the game, so \( M = 90 \).

4. We can set up a proportion to find \( W \): \[ \frac{90}{W} = \frac{3}{2} \]

5. Cross-multiply to solve for \( W \): \[ 3W = 90 \times 2 \] \[ 3W = 180 \]

6. Now, divide both sides by 3: \[ W = \frac{180}{3} = 60 \]

Thus, there were 60 women at the basketball game.

To justify, we can check the ratio:

• The ratio of men to women is \( 90:60 \).
• Simplifying that ratio: \[ \frac{90}{60} = \frac{3}{2} \] This matches the given ratio, confirming our calculation is correct.