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? (1 point) Responses 20a+5=70 20 A plus 5 is equal to 70 5a+20=70 5 A plus 20 is equal to 70 5a+70=20 5 A plus 70 is equal to 20 5a−20=70

Answer 1

To determine the age of Key, we can set up an equation based on the information provided. Let's denote the age of the oldest sibling as \( x \).

Since the siblings are born 2 years apart, we can define their ages as follows:
- Oldest sibling: \( x \)
- 2nd oldest: \( x - 2 \)
- 3rd sibling: \( x - 4 \)
- 4th sibling: \( x - 6 \)
- Youngest sibling (Key): \( x - 8 \)

Now, we can sum up their ages:
\[
x + (x - 2) + (x - 4) + (x - 6) + (x - 8) = 70
\]

This simplifies to:
\[
5x - 20 = 70
\]

To find the equation in terms of Key's age \( a \), we know Key's age is \( a = x - 8 \).

From \( 5x - 20 = 70 \), we can isolate \( x \):
\[
5x = 90 \quad \Rightarrow \quad x = 18
\]

Now substituting \( x = 18 \) back to find Key's age:
\[
a = x - 8 = 18 - 8 = 10
\]

However, to express this in terms of an equation to find \( a \), we can substitute \( a = x - 8 \) back into the equation derived from the sum of the ages:
\[
5(x - 8) + 20 = 70.
\]

So, finally the equivalent equation using \( a \) becomes:
\[
5a + 20 = 70.
\]

Thus, the correct equation to determine the age, \( a \), of Key is:
\[
\boxed{5a + 20 = 70}.
\]