The White Sox won 27 fewer than twice as many games as they lost. They played 162 regular season games. They won 99 and lost 63. Show steps. No
Let W be the number of games they won. Let L be the number of games they lost.
We know that L + W = 162 because that's how many games they played.
We know that W = 2L - 27 because the wins are equal to 27 less than twice the losses.
Find for one of the variables. We'll find for L by subtracting W from both sides.
L = 162-W
Now plug this into your other equation.
W = 2(162-W) - 27
W = 324 - 2W - 27
Add 2w to both sides
3W = 297
Divide both sides by 3
W = 99.
Now take W and plug it back into your original equation.
L + 99 = 162
Subtract 99 from both sides
L = 63
The problem can be solved ituitively analysing without Algebra. Since the number of won games is is 27 less than two times the lost games, 3times the lost games is 162 +27 =189. And so the lost games =189/3 =63 and won games =162-63 = 99. But for clarity we use algebra:
Let the lost games be x and won games be y. Then by the 1st condition, y = 2x-27.........(1). By the other condition given the total games played, x+y =162............ (2)
Substituting the value of y in (2) we get: x + (2x-27) = 162.Simplifying we get:
3x-27 =162 .
Add 27 to both sides
3x -27+27=162+27 . Simplify:
3x=189 . Divide by 3 both sides:
Therefore x=63. Substituting in (2) this value of x 63, we get:
63+y =162 Or y = 162-62 = 99.
So the lost games =162 which is 2 times the number of won games- 27 or
162 = 2*99-27 =198-27