Question

Santiago is eight years younger than Juan is today. If, in four years, Santiago will be half Juan’s age, how old is Santiago today? a) 1 b) 2 c) 3 d) 4

Answer 1

Let S be Santiago’s age
Let J be Juan’s age.

Since Santiago is 8 yrs younger than Juan, we can write

Equation 1: S = J-8

In 4 yrs, Santiago age will be S + 4,
In 4 yrs, Juan’s age will be J + 4.

Given:
In 4 yrs, Santiago will be half of Juan’s age, so ..

Equation 2: S+4=(J+4)/2

We know the value of S from equation 1. Substitute S=J-8 in equation 2, we get

J -8 + 4=(J+4 )/2

J-4 = (J+4 )/2

2( J- 4) =J + 4
2J-8 =J + 4
2J-J =8+ 4
J = 12

Substitute J= 12 in equation 1
S= 12-8
S = 4

So, Santiago’s age is 4 yrs today.

Answer 2

d) 4.

Explanation:

Let Santiago be x years old today.

Then Juan is x + 8 years old.

In 4 years Santiago will be x + 4 years.

In 4 years Juan will be x + 12 years.

From the given information:

x + 4 = 0.5(x + 12)

x = 0.5x + 6 - 4

0.5x = 2

x = 2 / 0.5

x = 4.