Esther and Tina have some stickers. If Esther gives 18 stickers to Tina, Tina will have 4 times the number of stickers as Esther. If Tina gives 27 stickers to Esther, Esther will have
25 as many stickers as Tina. How many stickers does Esther have at first?
|
Case 1 |
Case 2 |
|
Esther |
Tina |
Esther |
Tina |
Before |
7 u + 18 |
28 u - 18 |
10 u - 27 |
25 u + 27 |
Change |
- 18 |
+ 18 |
+ 27 |
- 27 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of stickers in both cases remains unchanged. Make the total number of stickers in both cases the same. LCM of 5 and 7 is 35.
Number of stickers that Esther had at first is the same in both cases.
10 u - 27 = 7 u + 18
10 u - 7 u = 18 + 27
3 u = 45
1 u = 15
Number of stickers that Esther had at first
= 7 u + 18
= 7 x 15 + 18
= 105 + 18
= 123
Answer(s): 123