The ratio of the number of cupcakes in Container K to the number of cupcakes in Container L was 7 : 5. 30% of the cupcakes in Container K and 0.9 of those in Container L were mocha. After transferring the cupcakes between the 2 boxes, the number of peach cupcakes in both boxes are the same. Likewise, the number of mocha cupcakes in both boxes are the same. If a total of 187 cupcakes were moved, how many more cupcakes were there in Container K than Container L at first?
Container K |
Container L |
7 u |
5 u |
Mocha |
Peach |
Mocha |
Peach |
2.1 u |
4.9 u |
4.5 u |
0.5 u |
+ 1.2 u |
- 2.2 u |
- 1.2 u |
+ 2.2 u |
3.3 u |
2.7 u |
3.3 u |
2.7 u |
Number of mocha cupcakes in Container K
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Number of peach cupcakes in Container K
= 7 u - 2.1 u
= 4.9 u
Number of mocha cupcakes in Container L
= 0.9 x 5 u
= 4.5 u
Number of peach cupcakes in Container L
= 5 u - 4.5 u
= 0.5 u
Number of mocha cupcakes in each box in the end
= (2.1 u + 4.5 u) ÷ 2
= 6.6 u ÷ 2
= 3.3 u
Number of peach cupcakes in each box in the end
= (4.9 u + 0.5 u) ÷ 2
= 5.4 u ÷ 2
= 2.7 u
Number of cupcakes moved
= 1.2 u + 2.2 u
= 3.4 u
3.4 u = 187
1 u = 187 ÷ 3.4 = 55
Number of more cupcakes in Container K than Container L at first
= 7 u - 5 u
= 2 u
= 2 x 55
= 110
Answer(s): 110