Math CentralQuandaries & Queries


Question from Valence, a parent:

Mary gave her sister 5/8 of her nuts. Her sister gave her friend 2/3 of the amount, and her cousin 1/3 of the remainder. If Mary's sister had 50 nuts left, how many nuts had Mary.

Hi Valence,

This type of problem is called working backwards. You start with the end of the process and work towards the beginning. I can help get you started.

Mary's sister had 50 after she gave 2/3 of her nuts to her friend and then 1/3 of what she had left to her cousin. After she gave some nuts to her friend she gave 1/3 of what was left to her cousin and thus she kept 2/3 of what was left which is 50 nuts. Suppose the number of nuts she had after giving some to her friend was $N$ then 2/3 of $N$ is 50, or $\frac23 \times N = 50.$ Thus $N = \frac32 \times 50 = 75.$ Thus Mary's sister had 75 nuts left after giving some to her friend.

Mary's sister gave 2/3 of her nuts to her friend and was left with 75 nuts. What fraction did mary's sister keep for herself? How many nuts did Mary's sister start with? How many nuts did Mary start with?

Once you have an answer check it by working forward through the process.

Write back if you need more assistance,

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