Emily and Zara have some scones each. If Emily gives Zara 21 scones, Emily will have
58 as many scones as Zara. If Emily gives Zara 8 scones, they will have an equal number of scones. How many scones does Zara have at first?
| |
Case 1 |
Case 2 |
| |
Emily |
Zara |
Emily |
Zara |
| Before |
5 u + 21 |
8 u - 21 |
6.5 u + 8 |
6.5 u - 8 |
| Change |
- 21 |
+ 21 |
- 8 |
+ 8 |
| After |
5 u |
8 u |
6.5 u |
6.5 u |
Total number of scones that Emily and Zara have
= 5 u + 8 u
= 13 u
Number of scones that Emily and Zara each has in the end is the same.
Number of scones that Emily and Zara each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u
Number of scones that Emily had at first is the same in Case 1 and Case 2.
6.5 u + 8 = 5 u + 21
6.5 u - 5 u = 21 - 8
0.5 u = 13
1 u = 13 ÷ 0.5 = 26
Number of scones that Zara has
= 8 u - 21
= 8 x 26 - 21
= 208 - 21
= 187
Answer(s): 187
