Natalie and Joelle have some coins. If Natalie gives 11 coins to Joelle, Joelle will have 4 times the number of coins as Natalie. If Joelle gives 122 coins to Natalie, Natalie will have
35 as many coins as Joelle. How many coins does Natalie have at first?
|
Case 1 |
Case 2 |
|
Natalie |
Joelle |
Natalie |
Joelle |
Before |
8 u + 11 |
32 u - 11 |
15 u - 122 |
25 u + 122 |
Change |
- 11 |
+ 11 |
+ 122 |
- 122 |
After |
1x8 = 8 u |
4x8 = 32 u |
3x5 = 15 u |
5x5 = 25 u |
The total number of coins in both cases remains unchanged. Make the total number of coins in both cases the same. LCM of 5 and 8 is 40.
Number of coins that Natalie had at first is the same in both cases.
15 u - 122 = 8 u + 11
15 u - 8 u = 11 + 122
7 u = 133
1 u = 19
Number of coins that Natalie had at first
= 8 u + 11
= 8 x 19 + 11
= 152 + 11
= 163
Answer(s): 163