Question P4–P5–P6 Suppose and swap
Today’s problem — free all day, every step. Every day has one.
Wei Yang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20c or 50c coin. His mother also put in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90.
Answer
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Suppose everything is one kind, then swap one at a time until the total is right.
In this one. When a total mixes coins you can count exactly with coins you cannot, take the countable ones out first — then the rest is a plain "suppose they are all the cheap one" problem, and each swap to the dearer coin buys back a fixed difference.
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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