Opal and Eva have some cupcakes each. If Opal gives Eva 17 cupcakes, Opal will have
12 as many cupcakes as Eva. If Opal gives Eva 4 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Eva have at first?
| |
Case 1 |
Case 2 |
| |
Opal |
Eva |
Opal |
Eva |
| Before |
1 u + 17 |
2 u - 17 |
1.5 u + 4 |
1.5 u - 4 |
| Change |
- 17 |
+ 17 |
- 4 |
+ 4 |
| After |
1 u |
2 u |
1.5 u |
1.5 u |
Total number of cupcakes that Opal and Eva have
= 1 u + 2 u
= 3 u
Number of cupcakes that Opal and Eva each has in the end is the same.
Number of cupcakes that Opal and Eva each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u
Number of cupcakes that Opal had at first is the same in Case 1 and Case 2.
1.5 u + 4 = 1 u + 17
1.5 u - 1 u = 17 - 4
0.5 u = 13
1 u = 13 ÷ 0.5 = 26
Number of cupcakes that Eva has
= 2 u - 17
= 2 x 26 - 17
= 52 - 17
= 35
Answer(s): 35
