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.

Question

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. \( 5a + 20 = 70 \)