Julian and Warren collected some marbles. If Julian gave Warren 53 marbles, both would have an equal number of marbles. If Warren gave Julian 37 marbles, Julian would have 6 times as many marbles as Warren. Find the number of marbles each of them had.
- Julian?
- Warren?
| Case 1 |
Case 2 |
| Julian |
Warren |
Julian |
Warren |
| 7 u + 53 |
7 u - 53 |
12 u - 37 |
2 u + 37 |
| - 53 |
+ 53 |
+ 37 |
- 37 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of marbles the same. LCM of 2 and 7 is 14.
The number of marbles that Warren had at first is the same in both cases.
7 u - 53 = 2 u + 37
7 u - 2 u = 53 + 37
5 u = 90
1 u = 90 ÷ 5 = 18
Number of marbles that Julian had
= 7 u + 53
= 7 x 18 + 53
= 179
(b)
Number of marbles that Warren had
= 7 u - 53
= 7 x 18 - 53
= 73
Answer(s): (a) 179; (b) 73
