At a concert, there were 1004 children and adults at first. During the interval, 14 adults and 27 of the children went home. The number of children remaining was 13 the number of adults remaining.
- How many children were at the concert at first?
- How many people remained at the concert after the interval?
Need a hint?
Put the children who stayed as 5 units, because 27 of them left. Then use the second sentence to find the adults who stayed.
Worked answer
- 27 of the children left, so 57 of the children remained. Let children remaining be 5 units, so children at first = 7 units.
- Children remaining is 13 of adults remaining, so adults remaining = 3 × 5 units = 15 units.
- 14 adults went home, so adults at first = 15 units + 14.
- Total at first: 7 units + 15 units + 14 = 22 units + 14 = 1004.
- 22 units = 1004 − 14 = 990, so 1 unit = 990 ÷ 22 = 45.
- (a) Children at first = 7 × 45 = 315.
- (b) People remaining = 5 units + 15 units = 20 units = 20 × 45 = 900.
Answer: 900 people
The mistake this question tests
Habit
Fraction of a remainder
Many pupils forget that the 14 adults who left are part of the 1004, so they divide 1004 by 22 units. The 14 must be taken away first.
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