Question

Four years ago, twice Athena's age was five less than her cousin's age. At present, the age of Athena's cousin is 18 years less than thrice Athena's age. What are their ages now?

If Athena's age 4 years ago is x, then her cousin's age 4 years ago is what? Is it that her cousin is older?

Answer 1

Athena's age is expressed as a function of the cousin's age, so it is usually easier to define the domain

Four years ago:
let the cousin's age be x
then Athena was 2x-5

present:
cousin ---- x+4
Athena ----- 2x-5 + 4 or 2x - 1

x+4 = 3(2x-1) - 18
x+4 = 6x - 3 - 18
25 = 5x
x = 5

subbing into my definitions:
the cousin is now 9 and Athena is now 9

mmmhhh, let's check this

4 years ago, Athena was 5 and the cousin was 5
Twice Athena's age would be 10, and 5 less would be 5, which is the cousin's age.

Now, three times Athena's age is 27 , less 18 is 9, which is the present age of the cousin

My answers are correct

Answer 2

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