SOLUTION: A is 20 years older than B. He is also 6 times as old as B. find their ages.

Question 124980: A is 20 years older than B. He is also 6 times as old as B. find their ages.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let X represent the age of A. And let Y represent the age of B.
.
The statement that A is 20 years older than B means that to equal B's age you have to subtract 20
from A's age. Taking 20 away from A's age is represented by the expression X - 20. This will
be equal to Y. In equation form this equality is written as:
.
X - 20 = Y
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The problem also tells you that A's age (X) is equal to 6 times B's age (Y). In equation form
this is:
.
X = 6Y
.
But from the first equation we know that X - 20 is the same as Y. So, in the second equation
we can replace that Y with X - 20. When we do that the second equation becomes:
.
X = 6(X - 20)
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Multiply out the right side by multiplying each of the terms inside the parentheses
by 6. When you do this multiplication this becomes:
.
X = 6X - 120
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You can get all the terms containing X to one side of this equation by getting rid of
the 6X on the right side. To do this, just subtract 6X from both sides of the equation.
Subtracting 6X from the right side eliminates the 6X on that side. Subtracting 6X from
the X on the left side results in that side becoming -5X. So by subtracting 6X from both
sides changes the equation to:
.
-5X = -120
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To solve for that equation you divide both sides of this equation by -5 to get:
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X = -120/-5 = 24
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This means that A is 24 years old. Since A is 20 years older than B, then B must be 4 years old.
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And you can also see that at age 24 A is 6 times older than B who is 4 years old.
.
The answers we got check out.
.
Hope this helps you to understand the problem.
.

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