P5 Math: Anna and Sue

Anna and Sue folded paper cranes to raise funds for an event. 1/3 of Anna's paper cranes was 16 more than 1/4 of Sue's paper cranes. After a few days, Anna folded more paper cranes and her total increased by 1/3. Sue had to throw away 1/2 of hers as they were torn. At the end, Anna had 82 paper cranes more than Sue. How many paper cranes were there in the end?

Solution:

At first
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Sue has 4u paper cranes. Why 4u ?
1/3 of Anna's paper cranes = u + 16
Total of Anna's paper cranes = 3 times (u + 16) = 3u + 48

After a few days
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Anna folded 1/3 more than her current paper cranes
1/3 of new paper cranes = u + 16
Now Anna has (u + 16) + (3u + 48) = 4u +64

Sue had to throw away 1/2 of her current paper cranes
1/2 of current paper cranes = 1/2 x 4u = 2u
Now Sue has 4u - 2u = 2u

At the end
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Anna had 82 paper cranes more than Sue
4u + 64 = 82 + 2u, 2u = 18, u = 9

Number of paper cranes at the end
Sue = 2u = 18
Anna = 4u + 64 = 100