Find the height of the stool.
Answer: Stool + cat = 85 and stool − cat = 25, so the stool is 55 cm high (and the cat 30 cm).
Step-by-step solution
Idea: Let the stool be s cm and the cat c cm tall. The left picture shows their heights added; the right picture shows the difference.
- Left picture: the cat sits on the stool, so s + c = 85 … (1).1 mark
- Right picture: the cat is under the stool and the stool is 25 cm taller: s − c = 25 … (2).1 mark
- (1) + (2): 2s = 110 ⇒ s = 55. (And c = 30.) The stool is 55 cm high.1 mark
The stool is 55 cm high (the cat is 30 cm tall).
Check: 55 + 30 = 85 ✓ and 55 − 30 = 25 ✓.
Answer to write in the exam
Let stool = s cm, cat = c cm
s + c = 85 … (1)
s − c = 25 … (2)
(1) + (2): 2s = 110 ⇒ s = 55
∴ Height of the stool = 55 cm
Common mistakes that cost marks
- Taking 85 − 25 = 60 as the stool’s height.
- Giving the cat’s height (30 cm) as the answer.
How this can come in the exam
Short answer (2 marks)
A book on a table reaches 98 cm; the table is 62 cm taller than the book standing on the floor. Find the table’s height.
Show answer
t + b = 98, t − b = 62 (1 mark) ⇒ 2t = 160 ⇒ t = 80 cm (1 mark).Try one yourself
A box on a shelf reaches 150 cm; the shelf is 90 cm taller than the box. Find the shelf height.
Show answer
s + b = 150, s − b = 90 ⇒ s = 120 cm.
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