 # Question

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?

```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.

```
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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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