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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# Question

# 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, thedifference at the start = difference at the end. So1 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 thedifference 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

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