Abi and Diana have some marbles. If Abi gives 13 marbles to Diana, Diana will have 4 times the number of marbles as Abi. If Diana gives 20 marbles to Abi, Abi will have
25 as many marbles as Diana. How many marbles does Abi have at first?
|
Case 1 |
Case 2 |
|
Abi |
Diana |
Abi |
Diana |
Before |
7 u + 13 |
28 u - 13 |
10 u - 20 |
25 u + 20 |
Change |
- 13 |
+ 13 |
+ 20 |
- 20 |
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 Abi had at first is the same in both cases.
10 u - 20 = 7 u + 13
10 u - 7 u = 13 + 20
3 u = 33
1 u = 11
Number of marbles that Abi had at first
= 7 u + 13
= 7 x 11 + 13
= 77 + 13
= 90
Answer(s): 90