Question

Last year,Peter was taller than Jane by 5cm.This year,Peter grew by 8cm and Jane grew by 5cm.If their total height this year is 282cm, what was Jane’s height this year?

Answer 1

Let Jane's height last year be \( j \) cm. Then, Peter's height last year would be \( j + 5 \) cm since Peter was taller than Jane by 5 cm.

This year, Jane grew by 5 cm, so her height this year is:
\[
j + 5 \ \text{cm}
\]

Peter grew by 8 cm, so his height this year is:
\[
(j + 5) + 8 = j + 13 \ \text{cm}
\]

The total height of Peter and Jane this year is given as 282 cm. Therefore, we set up the equation:
\[
(j + 5) + (j + 13) = 282
\]

Simplifying the left side:
\[
2j + 18 = 282
\]

Next, we isolate \( j \) by first subtracting 18 from both sides:
\[
2j = 282 - 18
\]
\[
2j = 264
\]

Now, divide by 2:
\[
j = 132
\]

Thus, Jane's height last year was 132 cm. To find Jane's height this year, we add the growth she experienced:
\[
132 + 5 = 137 \ \text{cm}
\]

Therefore, Jane's height this year is:
\[
\boxed{137} \ \text{cm}
\]