Question

Key is the youngest of 5 siblings. Starting with the oldest sibling, each sibling was born 2 years apart. Together, the siblings are 70 years old.

Which equation can be used to determine the age, a, of Key?

Answer 1

Let's denote the ages of the five siblings as follows:

1. Oldest sibling: \( a + 8 \)
2. Next sibling: \( a + 6 \)
3. Middle sibling: \( a + 4 \)
4. Second youngest sibling: \( a + 2 \)
5. Key (the youngest sibling): \( a \)

The siblings are 2 years apart in age, and since Key is the youngest, there are four siblings older than her. The sum of their ages equals 70 years old. We can set up the equation for the total age of the siblings:

\[
(a + 8) + (a + 6) + (a + 4) + (a + 2) + a = 70
\]

Now, simplify the left side of the equation:

\[
5a + 8 + 6 + 4 + 2 = 70
\]
\[
5a + 20 = 70
\]

Thus, the equation that can be used to determine Key's age \( a \) is:

\[
5a + 20 = 70
\]

Now, you can solve for \( a \) to find Key's age.