Sabrina and Abi have some marbles. If Sabrina gives 25 marbles to Abi, Abi will have 4 times the number of marbles as Sabrina. If Abi gives 8 marbles to Sabrina, Sabrina will have
25 as many marbles as Abi. How many marbles does Sabrina have at first?
|
Case 1 |
Case 2 |
|
Sabrina |
Abi |
Sabrina |
Abi |
Before |
7 u + 25 |
28 u - 25 |
10 u - 8 |
25 u + 8 |
Change |
- 25 |
+ 25 |
+ 8 |
- 8 |
After |
1x7 = 7 u |
4x7 = 28 u |
2x5 = 10 u |
5x5 = 25 u |
The total number of marbles in both cases remains unchanged. Make the total number of marbles in both cases the same. LCM of 5 and 7 is 35.
Number of marbles that Sabrina had at first is the same in both cases.
10 u - 8 = 7 u + 25
10 u - 7 u = 25 + 8
3 u = 33
1 u = 11
Number of marbles that Sabrina had at first
= 7 u + 25
= 7 x 11 + 25
= 77 + 25
= 102
Answer(s): 102