Math CentralQuandaries & Queries


Question from Skylar, a student:

A family is raking leaves. Betsy fills 3 bags to every 2 bags the Meri fills. After a while, Jim joins them. He fills 3 bags to every 2 bags that Betsy fills, but he only works half as long. When finished, they have completely filled 58 bags. If Meri takes 6 minutes to fill one bag, how long was she be raking leaves?


One possible strategy is to determine how many bags Meri filled, then multiply this by the time per bag.

Now let a variable, say b, equal the number of bags Meri filled.

Calculate how many bags Betsy filled for every bag Meri filled, and add them, as that is how many were filled in the given time.

Do the same for Jim but cut this number in half, as Jim only worked half as long.

Sum up the total number of bags filled by each.

Set equal to the given number, and solve for b.

This will be the number of bags Meri filled!


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