Rowan bought some vanilla and chocolate cupcakes in the ratio of 5:4. After Rowan’s classmates ate an equal number of the two types of cupcakes, there were 40% fewer chocolate than vanilla cupcakes. In the end, there were 152 cupcakes left. How many cupcake of each type were eaten?
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Answer
mr.tan
Let fill up a table to track what is happening.
We start from the End and go back to Start.
| Vanilla | Chocolate | Ratio V:C | Diff | |
| End ratio | 100% | 100%-40%=60% | 5:3 (8 parts) | – |
| End number = 152 | 5/8 x 152 = 95 | 3/8 x 152 = 57 | – | 95 – 57 = 38 |
| Start ratio | 5 units | 4 units | 5:4 (9 units) | 1 unit |
| Start numbers | 4 x 38 = 152 |
Since the number of eaten for both flavors are the same, the difference at the start = difference at the end. So 1 unit = 38. At the start, there were 4 x 38 = 152. So number of each type eaten is 152 - 57 = 95.
PS: This kind of question (where same number were increased or decreased for both categories) has the property that the difference between the categories does not change.
sushi88
Vanilla Chocolate
At first [u][u][u][u][u] [u][u][u][u]
2 x ATE ? ?
Left 5u-ATE 4u-ATE
Find ATE cupcakes in terms of u
0.6 (5u-ATE) = 4u- ATE (after eating, choc cupcake was 40% lesser than vanilla means 60%V=C)
3u – 0.6 ATE = 4u – ATE
0.4 ATE = u
ATE = 2.5u ===> 2 x ATE = 5u (equal number of cupcakes eaten for both types)
Vanila Chocolate
At first [u][u][u][u][u] [u][u][u][u]
2 x ATE [u][u][u][u][u]
Left <—-152—->
4u = 152
u = 38
Hence cupcake of each type eaten was 2.5u = 2.5(38) = 95