Jean has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 19 mini cupcakes left. If she packs 2 sweets and 3 mini cupcakes in each bag, there will be 29 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 + 19 |
2 p + 29 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
19 |
29 |
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 = 2 p + 29 --- (1)
1 u + 19 = 3 p
1 u = 3 p - 19 --- (2)
(2) = (1)
3 p - 19 = 2 p + 29
3 p - 2 p = 29 + 19
1 p = 48
Total number of sweets and mini cupcakes
= (2 p + 29) + 3 p
= 5 p + 29
= 5 x 48 + 29
= 240 + 29
= 269
Answer(s): 269
