Erika and Jen have some scones each. If Erika gives Jen 29 scones, Erika will have
14 as many scones as Jen. If Erika gives Jen 5 scones, they will have an equal number of scones. How many scones does Jen have at first?
| |
Case 1 |
Case 2 |
| |
Erika |
Jen |
Erika |
Jen |
| Before |
1 u + 29 |
4 u - 29 |
2.5 u + 5 |
2.5 u - 5 |
| Change |
- 29 |
+ 29 |
- 5 |
+ 5 |
| After |
1 u |
4 u |
2.5 u |
2.5 u |
Total number of scones that Erika and Jen have
= 1 u + 4 u
= 5 u
Number of scones that Erika and Jen each has in the end is the same.
Number of scones that Erika and Jen each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u
Number of scones that Erika had at first is the same in Case 1 and Case 2.
2.5 u + 5 = 1 u + 29
2.5 u - 1 u = 29 - 5
0.5 u = 24
1 u = 24 ÷ 0.5 = 48
Number of scones that Jen has
= 4 u - 29
= 4 x 48 - 29
= 192 - 29
= 163
Answer(s): 163
