# Question

Tim had 40% more muffins than Rael. Tim gave 20% of his muffins to Rael. Rael in return gave 50% of his muffins to Tim. In the end, Rael had 448 less muffins than Tim. How many muffins did Tim have at first?

 Storyline Tim Rael Tim had 40% more muffins than Rael 140u 100u Tim gave 20% (28u) to Rael 112u 128u Rael returned 50% (64u) to Tim 176u 64u
```Rael had 176u - 64u = 112u less muffins than Tim.
So 112u = 448 and u = 448/112 = 4.
Tim had 140 x 4 = 560 muffins at first.

Check: Just fill up the table with actual values```
 Storyline Tim Rael Tim had 40% more muffins than Rael 560 400 Tim gave 20% (112) to Rael 448 512 Rael returned 50% (256) to Tim 704 256

Difference = 704 – 256 = 448.

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Tim        [u][(2/5)u]              40% more = (2/5)u

Rael       [u]

Removing the fraction, the model diagram can be represented as

Tim        [5u][2u]             Total   =  7u

Rael       [5u]

Tim gave 0.2(7u) = 1.4u to Rael

Tim        [5u][0.6u]          New total = 5.6u

Rael       [5u][1.4u]          New total = 6.4u

Rael gave 0.5(6.4u)= 3.2u back to Tim

Tim        [5u][0.6u][3.2u]         New total = 8.8u

Rael       [3.2u]

So 8.8u3.2 u = 448

5.6u = 448  => u = 80

Hence total muffins Tim has at first = 7u = 7 (80) = 560

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