Zaid planned a family celebration. He spent 27 of the money he had saved on decorations. He then spent 35 of the remaining money on a band, food and party games. The band cost 4 times as much as the party games. The food cost 14 as much as the party games. The decorations cost $20 more than the party games.
- What fraction of Zaid's original savings remained after he paid for the decorations?
- What fraction of the money spent on the band, food and party games was spent on food?
- How much did the food cost?
Need a hint?
First find what fraction of the original savings went to the band, food and party games. Then compare the fractions for the decorations and party games using the $20 difference.
Worked answer
- After paying for decorations, Zaid had 1 - 27 = 57 of his original savings left.
- The amount spent on the band, food and party games was 35 × 57 = 37 of the original savings.
- Band:party games:food = 16:4:1, so food was 121 of these three costs.
- Food was 121 × 37 = 149 of the original savings.
- The party games cost 4 × 149 = 449 of the original savings.
- The difference between the fractions for decorations and party games was 27 - 449 = 1049.
- Original savings = $20 ÷ 1049 = $98.
- Food = 149 × $98 = $2.
Answer: $2
The mistake this question tests
Habit
Fraction of a remainder
A common mistake is to take 35 of Zaid's original savings instead of 35 of the savings remaining after the decorations.
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