Vanessa and Barbara have some marbles. If Vanessa gives 28 marbles to Barbara, Barbara will have 5 times the number of marbles as Vanessa. If Barbara gives 57 marbles to Vanessa, Vanessa will have
35 as many marbles as Barbara. How many marbles does Vanessa have at first?
|
Case 1 |
Case 2 |
|
Vanessa |
Barbara |
Vanessa |
Barbara |
Before |
4 u + 28 |
20 u - 28 |
9 u - 57 |
15 u + 57 |
Change |
- 28 |
+ 28 |
+ 57 |
- 57 |
After |
1x4 = 4 u |
5x4 = 20 u |
3x3 = 9 u |
5x3 = 15 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 6 and 8 is 24.
Number of marbles that Vanessa had at first is the same in both cases.
9 u - 57 = 4 u + 28
9 u - 4 u = 28 + 57
5 u = 85
1 u = 17
Number of marbles that Vanessa had at first
= 4 u + 28
= 4 x 17 + 28
= 68 + 28
= 96
Answer(s): 96