Question

a baseball team played 140 regular season games. the ratio of the number of games they won to the number of games they lost was \\(\frac{5}{2}\\). how many games did they win? how many games did they lose?
the team won \\(\square\\) games. (type a whole number.)

Explanation:

Step1: Define variables and ratio sum

Let the number of games won be \( 5x \) and lost be \( 2x \) (since the ratio of won to lost is \( \frac{5}{2} \), so total parts \( 5 + 2 = 7 \)). The total games are 140, so \( 5x + 2x = 140 \).

Step2: Solve for x

Combine like terms: \( 7x = 140 \). Divide both sides by 7: \( x = \frac{140}{7} = 20 \).

Step3: Find games won

Substitute \( x = 20 \) into \( 5x \): \( 5 \times 20 = 100 \).

Step4: Find games lost (optional, but for completeness)

Substitute \( x = 20 \) into \( 2x \): \( 2 \times 20 = 40 \). (But the question here asks for games won, so we focus on that.)

Answer:

100