Diana and Fanny have some marbles. If Diana gives 28 marbles to Fanny, Fanny will have 5 times the number of marbles as Diana. If Fanny gives 98 marbles to Diana, Diana will have
23 as many marbles as Fanny. How many marbles does Diana have at first?
|
Case 1 |
Case 2 |
|
Diana |
Fanny |
Diana |
Fanny |
Before |
5 u + 28 |
25 u - 28 |
12 u - 98 |
18 u + 98 |
Change |
- 28 |
+ 28 |
+ 98 |
- 98 |
After |
1x5 = 5 u |
5x5 = 25 u |
2x6 = 12 u |
3x6 = 18 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 5 is 30.
Number of marbles that Diana had at first is the same in both cases.
12 u - 98 = 5 u + 28
12 u - 5 u = 28 + 98
7 u = 126
1 u = 18
Number of marbles that Diana had at first
= 5 u + 28
= 5 x 18 + 28
= 90 + 28
= 118
Answer(s): 118