Ratio: Cupcakes and Beef Pies

 In a bakery, the ratio of the number of cupcakes to the number of beef pies was 4:5. When 5/8 of the cupcakes were sold and another 12 beef pies were added on the shelf, the new ratio of cupcakes to beef pies was 1:4.

(1) How many cupcakes were eaten?

(2) How many cupcakes and beef pies were there at first?

Solution:

Use model to illustrate the solution

From the second figure, the additional pies are equal to 2u.

2u = 12 --> u = 6.

1. Number of cupcakes eaten = 5u = 30 pieces.
2. Number of cupcakes and pies at first = 8u + 10u = 18u = 108 pieces.