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 3
-
4
how many games did they win?
how many games did they lose?
I just need help on a better way of understanding it.
To find the number of games the baseball team won and lost, we will use the given ratio of wins to losses, which is 3/4.
First, let's assign variables to the number of wins and losses. Let's say the number of wins is W and the number of losses is L.
According to the ratio, we have the equation:
W/L = 3/4
To solve for the values of W and L, we can cross-multiply:
W * 4 = L * 3
Now, let's think about the total number of games played in the regular season, which is given as 140 games. We know that the number of wins plus the number of losses should equal the total number of games:
W + L = 140
From our previous equation, we can substitute W * 4 with L * 3 into the second equation:
L * 4 * 4/3 + L = 140
Simplifying this equation, we get:
16L/3 + L = 140
To eliminate the fraction, we can multiply the whole equation by 3:
16L + 3L = 420
19L = 420
Now, we can solve this equation for L:
L = 420/19 ≈ 22.11
Since we cannot have a fraction of a game, we round L to the nearest whole number:
L ≈ 22
To find the number of wins, we substitute the value of L back into the equation:
W = L * 3/4
W = 22 * 3/4
W = 66/4 ≈ 16.5
Again, we round W to the nearest whole number:
W ≈ 17
Therefore, the baseball team won approximately 17 games and lost approximately 22 games.
To determine the number of games the baseball team won and lost, we first need to find a common denominator for the given ratio, which is 3/4. The common denominator is 4, so we have:
Winning ratio = 3/4
Losing ratio = 1 (since 4 - 3 = 1)
Now, we can set up an equation using the number of games played:
Let W represent the number of games won.
Let L represent the number of games lost.
According to the given ratio, we have:
W/L = 3/4
Cross-multiplying, we get:
4W = 3L
Since the team played a total of 140 games, we can write another equation based on that:
W + L = 140
Now, we can solve this system of equations to find W and L.
Multiplying the second equation by 4, we have:
4W + 4L = 560
Substituting the value of 4W from the first equation into the second equation, we get:
3L + 4L = 560
7L = 560
L = 80
Substituting the value of L into the first equation, we can find W:
4W = 3L
4W = 3(80)
4W = 240
W = 60
Therefore, the baseball team won 60 games and lost 80 games.
3/7 = L/140
Cross multiply and solve for L.
7L = 420
L = 60 games lost