Zara and Olivia have some marbles. If Zara gives 11 marbles to Olivia, Olivia will have 4 times the number of marbles as Zara. If Olivia gives 66 marbles to Zara, Zara will have
35 as many marbles as Olivia. How many marbles does Zara have at first?
|
Case 1 |
Case 2 |
|
Zara |
Olivia |
Zara |
Olivia |
Before |
8 u + 11 |
32 u - 11 |
15 u - 66 |
25 u + 66 |
Change |
- 11 |
+ 11 |
+ 66 |
- 66 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 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 8 is 40.
Number of marbles that Zara had at first is the same in both cases.
15 u - 66 = 8 u + 11
15 u - 8 u = 11 + 66
7 u = 77
1 u = 11
Number of marbles that Zara had at first
= 8 u + 11
= 8 x 11 + 11
= 88 + 11
= 99
Answer(s): 99