Question 387535: The sum of Weng's age and Yayo's age is 20 yrs. In one year, Weng's age will be nine times Yayo's age one yr. ago. Find their present ages.
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! The sum of Weng's age and Yayo's age is 20 yrs. In one year, Weng's age will be nine times Yayo's age one yr. ago. Find their present ages.
First, we'll assign variables to both ages.
let W=Weng's age
let Y=Yato's age
Then, we'll come up with two equations to solve our two variables.
The sum of Weng's age and Yayo's age is 20 yrs. So, we have our first equation:
W + Y = 20
Solving this equation for W (it could be Y but we chose one at random):
W = 20 - Y
We have two variables, so we need another equation. We also know that in one year,
Weng's age will be nine times Yayo's age one yr. ago. In one year, Weng's age will be
W + 1. One year ago, Yato's age was Y - 1. We also know that the the first expression
is nine times the second, so:
W + 1 = 9(Y - 1) or
W + 1 = 9Y - 9
Substituting our value of W in from the first equation:
(20 - Y) + 1 = 9Y - 9
20 - Y + 1 = 9Y - 9
21 - Y = 9Y - 9
Adding 9 to both sides:
21 + 9 - Y = 9Y - 9 + 9
30 - Y = 9Y
Now adding Y to both sides:
30 - Y + Y = 9Y + Y
30 = 10Y
3 = Y
And substituting the value of Y into our first equation,
W = 20 - Y
W = 20 - 3
W = 17
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