Jade has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 26 mini cupcakes left. If she packs 3 sweets and 4 mini cupcakes in each bag, there will be 25 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 + 26 |
3 p + 25 |
4 p |
Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
After |
0 |
26 |
25 |
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 + 25 --- (1)
1 u + 26 = 4 p
1 u = 4 p - 26 --- (2)
(2) = (1)
4 p - 26 = 3 p + 25
4 p - 3 p = 25 + 26
1 p = 51
Total number of sweets and mini cupcakes
= (3 p + 25) + 4 p
= 7 p + 25
= 7 x 51 + 25
= 357 + 25
= 382
Answer(s): 382