Question P4–P5–P6 Suppose and swap
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At a school lunch, there are 84 bowls of soup for 61 people made up of teachers and students. Each teacher eats 3 bowls of soup, and every 4 students share 1 bowl. How many teachers and how many students are there?
Answer
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Suppose everything is one kind, then swap one at a time until the total is right.
In this one. Count in quarter-bowls so every amount is a whole number — then suppose all 61 are students and swap them into teachers one at a time, each swap adding exactly 12 − 1 = 11 quarters.
Two kinds of thing are mixed together with a known total count and a known total of something else, such as legs or sweets, and neither kind's count is given on its own.
Children lose track of whether a swap adds to the total or takes away from it. Compare the starting total with the target first, then swap in the direction that closes the gap.
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