At a bookshop, there were equal numbers of novels, poetry books and picture books at first. After 15 novels were sold, some poetry books and picture books were also sold, leaving 80 books. There were twice as many novels left as picture books, and the number of poetry books left was 8 more than the number of picture books left. How many poetry books were there at first?
- 18
- 26
- 36
- 51
Need a hint?
Let the picture books left be 1 unit and write the novels and poetry books left in units. Then add the 15 novels sold to find the original equal number.
Worked answer
- Let the number of picture books left be 1 unit.
- Then 2 units of novels and 1 unit + 8 poetry books were left.
- 80 books were left, so 4 units + 8 = 80, and 4 units = 72.
- 1 unit = 72 ÷ 4 = 18. So 36 novels and 18 + 8 = 26 poetry books were left.
- At first there were 36 + 15 = 51 novels, and there were equal numbers of each kind.
- So there were 51 poetry books at first.
Answer: 51 books
The mistake this question tests
Habit
Calculation slip
A common mistake is to stop after finding the number of poetry books left, which is 26. The question asks for the number at first, before any books were sold.
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