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 the ages of the five siblings be represented as follows:

- Oldest sibling: \( a + 8 \) (Key is the youngest, so the oldest is 8 years older)
- Second oldest: \( a + 6 \)
- Middle sibling: \( a + 4 \)
- Second youngest: \( a + 2 \)
- Key (youngest): \( a \)

We know all siblings together are 70 years old, so we can set up the equation:

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

Combining like terms:

\[
5a + 20 = 70
\]

To isolate \( a \):

\[
5a = 70 - 20
\]
\[
5a = 50
\]
\[
a = 10
\]

Thus, the equation \( 5a + 20 = 70 \) can be used to determine the age \( a \) of Key.