Hilda and Zara have some erasers. If Hilda gives 18 erasers to Zara, Zara will have 3 times the number of erasers as Hilda. If Zara gives 15 erasers to Hilda, Hilda will have
23 as many erasers as Zara. How many erasers does Hilda have at first?
|
Case 1 |
Case 2 |
|
Hilda |
Zara |
Hilda |
Zara |
Before |
5 u + 18 |
15 u - 18 |
8 u - 15 |
12 u + 15 |
Change |
- 18 |
+ 18 |
+ 15 |
- 15 |
After |
1x5 = 5 u |
3x5 = 15 u |
2x4 = 8 u |
3x4 = 12 u |
The total number of erasers in both cases remains unchanged. Make the total number of erasers in both cases the same. LCM of 4 and 5 is 20.
Number of erasers that Hilda had at first is the same in both cases.
8 u - 15 = 5 u + 18
8 u - 5 u = 18 + 15
3 u = 33
1 u = 11
Number of erasers that Hilda had at first
= 5 u + 18
= 5 x 11 + 18
= 55 + 18
= 73
Answer(s): 73