A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was four thirds . How many games did they? win? How many games did they? lose?
The Correct Answer and Explanation is:
Let’s break down the problem systematically:
We are told that the baseball team played a total of 154 games, and the ratio of games won to games lost is 4:3. This means that for every 4 games they won, they lost 3 games.
Step 1: Define Variables
Let:
- WWW be the number of games won
- LLL be the number of games lost
We are given that the total number of games played is 154, so:W+L=154W + L = 154W+L=154
We are also told the ratio of wins to losses is 4:3. This means:WL=43\frac{W}{L} = \frac{4}{3}LW=34
Step 2: Express Wins in Terms of Losses
From the ratio WL=43\frac{W}{L} = \frac{4}{3}LW=34, we can express the number of wins as:W=43LW = \frac{4}{3}LW=34L
Step 3: Substitute in the Total Games Equation
Substitute W=43LW = \frac{4}{3}LW=34L into the equation W+L=154W + L = 154W+L=154:43L+L=154\frac{4}{3}L + L = 15434L+L=154
Step 4: Solve for LLL
To solve for LLL, first combine the terms on the left-hand side:43L+33L=154\frac{4}{3}L + \frac{3}{3}L = 15434L+33L=15473L=154\frac{7}{3}L = 15437L=154
Multiply both sides by 3 to eliminate the fraction:7L=4627L = 4627L=462
Now, divide by 7:L=66L = 66L=66
Step 5: Calculate the Number of Wins
Now that we know L=66L = 66L=66, we can find WWW using the equation W=43LW = \frac{4}{3}LW=34L:W=43×66=88W = \frac{4}{3} \times 66 = 88W=34×66=88
Final Answer:
- The team won 88 games.
- The team lost 66 games.
Explanation:
This problem involves setting up a ratio equation based on the information provided and solving a system of equations. The ratio of wins to losses is 4:3, which allowed us to express the number of wins in terms of losses. By substituting this into the total games equation, we were able to solve for the number of games lost, and then find the number of games won.
