Kylie has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 13 mini cupcakes left. If she packs 3 sweets and 4 mini cupcakes in each bag, there will be 12 sweets left. How many sweets and mini cupcakes does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Mini Cupcakes |
Sweets |
Mini Cupcakes |
| Before |
1 u |
1 u + 13 |
3 p + 12 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
13 |
12 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of mini cupcakes at first is also the same for Case 1 and 2.
1 u = 3 p + 12 --- (1)
1 u + 13 = 4 p
1 u = 4 p - 13 --- (2)
(2) = (1)
4 p - 13 = 3 p + 12
4 p - 3 p = 12 + 13
1 p = 25
Total number of sweets and mini cupcakes
= (3 p + 12) + 4 p
= 7 p + 12
= 7 x 25 + 12
= 175 + 12
= 187
Answer(s): 187
