Age difference word problem

Question

Julia's age now is half that of Nicola's. One year from now, Julia's age will be three-fourth of Nicola's present age. Nicola is now n years old. What is the value of n?

Answer 1

We're told to use n for Nicole's age. Let's use j for Julia's age.

From the first sentence, j=1/2 n

From the 2nd sentence, j+1 = 3/4n. or j = 3/4 n - 1

We now have two equations which are equal to j, so using substitution, they are equal to one another.

1/2 n = 3/4 n - 1

Subtract 3/4 n from both sides

-1/4 n = -1

Multiply both sides by -4

n = 4

Nicole is 4 years old.

Julia is half of Nicole's age, so she Is 2 years old.