SOLUTION: An older person is eight years older than seven times the age of a young person. The sum of their ages is 40. Find their ages.

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Question 1057338: An older person is eight years older than seven times the age of a young person. The sum of their ages is 40. Find their ages.
Answer by solve_for_x(190) (Show Source):
You can put this solution on YOUR website!
Let x represent the age of the younger person.

Then, since the older person is "eight years older than seven times" the younger person, the older
person's age is given by:

7x + 8

Since the sum of the ages must be 40, you can write:

(7x + 8) + x = 40

Collecting like terms on the left gives:

8x + 8 = 40

Subtracting 8 from both sides leaves:

8x = 32

Dividing by 8 then gives:

x = 4

Since x is the age of the younger person, you know that the younger person is 4 years old.

From that, substitute 4 in place of x in the expression 7x + 8 to get the older person's age...which I'll leave to you to complete.