Problem 7

Explanation

Let:

• $a =$ current age of the younger sibling
• $k =$ current age of the older sibling

First Condition Analysis

Seven years ago, the sum of the ages of the older sibling and the younger sibling was $26$ years.

The mathematical model is:

Second Condition Analysis

Four years from now, twice the age of the older sibling is equal to twice the age of the younger sibling plus eight years.

The mathematical model is:

Finding the Younger Sibling's Age

We eliminate equation $(1)$ and $(2)$ to find the value of $a$.

We subtract the second equation from the first: $(k+a) - (k-a) = 2a$ and $40 - 4 = 36$.

Thus, the current age of the younger sibling is $18$ years.

Therefore, the younger sibling is $18$ years old.