Pedro is 4 years older than Juan. Five times Juan's age is three times Pedro's age. What are their ages? Let $P$ be Pedro's age and $J$ be Juan's age. We are given two equations: $P = J + 4$ $5J = 3P$

1. Problem Description

Pedro is 4 years older than Juan. Five times Juan's age is three times Pedro's age. What are their ages?

Let $P$ be Pedro's age and $J$ be Juan's age. We are given two equations:

$P = J + 4$

$5J = 3P$

2. Solution Steps

We have a system of two equations with two variables:

$P = J + 4$ (Equation 1)

$5J = 3P$ (Equation 2)

Substitute Equation 1 into Equation 2:

$5J = 3(J + 4)$

$5J = 3J + 12$

$5J - 3J = 12$

$2J = 12$

$J = \frac{12}{2}$

$J = 6$

Now, substitute $J = 6$ into Equation 1:

$P = 6 + 4$

$P = 10$

So, Juan is 6 years old and Pedro is 10 years old.

Check if the solution satisfies both equations:

Equation 1: $10 = 6 + 4$, which is true.

Equation 2: $5(6) = 3(10)$, so $30 = 30$, which is true.

3. Final Answer

Juan is 6 years old, and Pedro is 10 years old.