Jean and Emma have some buttons. If Jean gives 18 buttons to Emma, Emma will have 5 times the number of buttons as Jean. If Emma gives 22 buttons to Jean, Jean will have
35 as many buttons as Emma. How many buttons does Jean have at first?
| |
Case 1 |
Case 2 |
| |
Jean |
Emma |
Jean |
Emma |
| Before |
4 u + 18 |
20 u - 18 |
9 u - 22 |
15 u + 22 |
| Change |
- 18 |
+ 18 |
+ 22 |
- 22 |
| After |
1x4 =
4 u |
5x4 =
20 u |
3x3 =
9 u |
5x3 =
15 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 6 and 8 is 24.
Number of buttons that Jean had at first is the same in both cases.
9 u - 22 = 4 u + 18
9 u - 4 u = 18 + 22
5 u = 40
1 u = 8
Number of buttons that Jean had at first
= 4 u + 18
= 4 x 8 + 18
= 32 + 18
= 50
Answer(s): 50
