Michael and Sam had some buttons in the ratio of 8 : 5. Sam and Riordan had some buttons in the ratio of 2 : 1. Michael sold 33 buttons to Riordan and ended up with half the number of buttons Sam had. How many buttons did Riordan have in the end?
| Michael |
Sam |
Riordan |
| 8x2 |
5x2 |
|
| |
2x5 |
1x5 |
| 16 u |
10 u |
5 u |
The number of buttons that Sam had at first is repeated. Make the number of buttons that Sam had at first the same. LCM of 5 and 2 is 10.
| |
Michael |
Sam |
Riordan |
| Before |
16 u |
10 u |
5 u |
| Change |
- 33 |
|
+ 33 |
| After |
5 u |
10 u |
5 u + 33 |
Number of buttons that Michael had in the end
= 10 u ÷ 2
= 5 u
Number of buttons that Michael sold to Riordan
= 16 u - 5 u
= 11 u
11 u = 33
1 u = 33 ÷ 11 = 3
Number of buttons that Riordan had in the end
= 5 u + 33
= 5 x 3 + 33
= 15 + 33
= 48
Answer(s): 48
