Multi-step Equations Quick Check

Question

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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+70=20
5 A plus 70 is equal to 20

5a+20=70
5 A plus 20 is equal to 70

5a−20=70

Answer 1

To solve the problem, let's first clarify the details:

1. Key is the youngest of 5 siblings.
2. Each sibling is 2 years apart in age.
3. The total age of all siblings is 70 years.

Let’s assign ages based on Key's age, which we'll call \( a \):

• If Key is \( a \) years old, then the ages of the siblings are:
  • Sibling 1 (oldest) = \( a + 8 \) (Key's age + 4 siblings × 2 years each)
  • Sibling 2 = \( a + 6 \)
  • Sibling 3 = \( a + 4 \)
  • Sibling 4 = \( a + 2 \)
  • Key = \( a \)

Now, to find the total age of all siblings:

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

Simplifying this gives:

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

Therefore, the correct equation for determining the age \( a \) of Key is:

5a + 20 = 70

So the answer is the third option:

5a + 20 = 70