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?
A. 5a+70=20
B. 20a+5=70
C. 5a+20=70
D. 5a-20=70

Answer 1

To solve the problem, first, let's define the ages of the siblings:

1. Let \( a \) be the age of Key (the youngest sibling).
2. Since the siblings are 2 years apart, the ages of the other siblings will be:
- Oldest sibling: \( a + 8 \)
- Second oldest: \( a + 6 \)
- Middle sibling: \( a + 4 \)
- Second youngest: \( a + 2 \)

Now, we can express the total age of all 5 siblings:

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

Combining the terms, we have:

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

Calculating the sum of the numbers:

\[
2 + 4 + 6 + 8 = 20
\]

So the equation simplifies to:

\[
5a + 20 = 70
\]

To isolate \( a \), you would subtract 20 from both sides:

\[
5a = 70 - 20
\]

\[
5a = 50
\]

Now, divide both sides by 5:

\[
a = 10
\]

Hence, the equation that can be used to determine the age of Key is:

**C. \( 5a + 20 = 70 \)**