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?
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mr.tan
| 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.
sushi88
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 8.8u – 3.2 u = 448
5.6u = 448 => u = 80
Hence total muffins Tim has at first = 7u = 7 (80) = 560