Question 1190483: A woman is older than her daughter by 25 years. Three years ago, the ratio of their ages was 3:1. Find their present ages. Found 2 solutions by VFBundy, greenestamps:Answer by VFBundy(438) (Show Source):
You can put this solution on YOUR website! Woman's age = W
Daughter's age = D Make two equations:
W = D + 25
W - 3 = 3(D - 3) Simplify the second equation:
W = D + 25
W - 3 = 3D - 9 Move the variables to left side and the constants to right side:
W - D = 25
W - 3D = -6 Multiply the first equation by -3:
-3W + 3D = -75
W - 3D = -6 Add the equations together:
-2W = -81 Solve for W:
W = 40.5 Substitute W = 40.5 into either of the original equations:
W = D + 25
40.5 = D + 25 Solve for D:
D = 15.5
Woman's age = W = 40.5
Daughter's age = D = 15.5 Check it: "A woman is older than her daughter by 25 years."
40.5 is 25 years older than 15.5. "Three years ago, the ratio of their ages was 3:1."
Three years ago, the woman was 37.5 and the daughter was 12.5. The ratio of 37.5 to 12.5 is 3:1.
