Mei made some jam and filled two sizes of jars: large jars and small jars. She filled 3 large jars and 5 small jars with 8 kg of jam. With the remaining jam she could not fill another large jar, as she was short of 250 g of jam. Instead, she filled another small jar and had 150 g of jam left over.
- How many grams of jam are in one small jar? [2 marks]
- How many kilograms of jam did Mei make? [1 mark]
Need a hint?
Write the leftover jam two ways: as 'short of 250 g for a large jar' and as '150 g left after a small jar'. Set these equal.
Worked answer
- (a) Let the small jar hold S g and the large jar hold L g. Then 3L + 5S = 8000.
- The leftover jam is L − 250 g, and it is also S + 150 g, so L = S + 400.
- Replace L: 3(S + 400) + 5S = 8000, so 8S + 1200 = 8000.
- 8S = 6800, so S = 850. One small jar holds 850 g.
- (b) Large jar = 850 + 400 = 1250 g. Jam in jars = 3 × 1250 + 5 × 850 = 3750 + 4250 = 8000 g.
- Leftover = 1250 − 250 = 1000 g. Total = 8000 + 1000 = 9000 g = 9 kg.
The mistake this question tests
Converting units (kg, ℓ, m, cm³)
Pupils add 8 kg and the leftover amount without converting the 250 g and 150 g clues into the same unit, or they forget that the leftover is the same in both clues.
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