Gem and Anna have some scones each. If Gem gives Anna 34 scones, Gem will have
16 as many scones as Anna. If Gem gives Anna 10 scones, they will have an equal number of scones. How many scones does Anna have at first?
| |
Case 1 |
Case 2 |
| |
Gem |
Anna |
Gem |
Anna |
| Before |
1 u + 34 |
6 u - 34 |
3.5 u + 10 |
3.5 u - 10 |
| Change |
- 34 |
+ 34 |
- 10 |
+ 10 |
| After |
1 u |
6 u |
3.5 u |
3.5 u |
Total number of scones that Gem and Anna have
= 1 u + 6 u
= 7 u
Number of scones that Gem and Anna each has in the end is the same.
Number of scones that Gem and Anna each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u
Number of scones that Gem had at first is the same in Case 1 and Case 2.
3.5 u + 10 = 1 u + 34
3.5 u - 1 u = 34 - 10
0.5 u = 24
1 u = 24 ÷ 0.5 = 48
Number of scones that Anna has
= 6 u - 34
= 6 x 48 - 34
= 288 - 34
= 254
Answer(s): 254
