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| Math Central | Quandaries & Queries |
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Question from Eileen, a parent: Caslin has a total of 50 red beans and green beans. If she trades 1 red bean for 4 green beans, she will have 113 green beans, how may red beans and green beans does she have? |
Hi Eileen,
The subject line of your email was guess and check so let's try it that way.
Suppose 25 of the beans are red and 25 are green. She trades each of the red beans for 4 green beans so she gets 25 × 4 = 100 green beans for the red beans. She already has 25 green beans so now she has 100 + 25 = 125 which is too many. She must have started with fewer red beans.
Suppose 20 of the beans are red and 30 are green. She trades each of the red beans for 4 green beans so she gets 20 × 4 = 80 green beans for the red beans. She already has 30 green beans so now she has 80 + 30 = 110 which is too few. She must have started with more than 20 red beans but fewer than 25.
What's your next guess?
Penny
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