Mary and Xylia have some buttons. If Mary gives 38 buttons to Xylia, Xylia will have 4 times the number of buttons as Mary. If Xylia gives 88 buttons to Mary, Mary will have
35 as many buttons as Xylia. How many buttons does Mary have at first?
|
Case 1 |
Case 2 |
|
Mary |
Xylia |
Mary |
Xylia |
Before |
8 u + 38 |
32 u - 38 |
15 u - 88 |
25 u + 88 |
Change |
- 38 |
+ 38 |
+ 88 |
- 88 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 u |
The total number of buttons in both cases remains unchanged. Make the total number of buttons in both cases the same. LCM of 5 and 8 is 40.
Number of buttons that Mary had at first is the same in both cases.
15 u - 88 = 8 u + 38
15 u - 8 u = 38 + 88
7 u = 126
1 u = 18
Number of buttons that Mary had at first
= 8 u + 38
= 8 x 18 + 38
= 144 + 38
= 182
Answer(s): 182