Question

Jenny is eight years older than twice her cousin Sue’s age. The sum of their ages is less than 32.

What is the greatest age that Sue could be?



Responses

7
7

8
8

9
9

10

Answer 1

Let Sue's age be \( s \). Then Jenny's age can be expressed as:

\[
j = 2s + 8
\]

According to the problem, the sum of their ages is less than 32, which gives us the inequality:

\[
s + j < 32
\]

Substituting \( j \) into the inequality, we get:

\[
s + (2s + 8) < 32
\]

Simplifying this, we have:

\[
3s + 8 < 32
\]

Subtracting 8 from both sides:

\[
3s < 24
\]

Dividing both sides by 3:

\[
s < 8
\]

Since \( s \) must be a whole number, the greatest possible age for Sue that satisfies this inequality is \( 7 \).

Thus, the greatest age that Sue could be is:

\[
\boxed{7}
\]