Usha and Dana have some cupcakes each. If Usha gives Dana 7 cupcakes, Usha will have
16 as many cupcakes as Dana. If Usha gives Dana 5 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Usha have at first?
| |
Case 1 |
Case 2 |
| |
Usha |
Dana |
Usha |
Dana |
| Before |
1 u + 7 |
6 u - 7 |
3.5 u + 5 |
3.5 u - 5 |
| Change |
- 7 |
+ 7 |
- 5 |
+ 5 |
| After |
1 u |
6 u |
3.5 u |
3.5 u |
Total number of cupcakes that Usha and Dana have
= 1 u + 6 u
= 7 u
Number of cupcakes that Usha and Dana each has in the end is the same.
Number of cupcakes that Usha and Dana each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u
Number of cupcakes that Usha had at first is the same in Case 1 and Case 2.
3.5 u + 5 = 1 u + 7
3.5 u - 1 u = 7 - 5
0.5 u = 2
1 u = 2 ÷ 0.5 = 4
Number of cupcakes that Usha has
= 1 u + 7
= 1 x 4 + 7
= 4 + 7
= 11
Answer(s): 11
