Caden and Wesley had some buttons in the ratio of 4 : 3. Wesley and Zeph had some buttons in the ratio of 8 : 1. Caden sold 220 buttons to Zeph and ended up with half the number of buttons Wesley had. How many buttons did Zeph have in the end?
| Caden |
Wesley |
Zeph |
| 4x8 |
3x8 |
|
| |
8x3 |
1x3 |
| 32 u |
24 u |
3 u |
The number of buttons that Wesley had at first is repeated. Make the number of buttons that Wesley had at first the same. LCM of 3 and 8 is 24.
| |
Caden |
Wesley |
Zeph |
| Before |
32 u |
24 u |
3 u |
| Change |
- 220 |
|
+ 220 |
| After |
12 u |
24 u |
3 u + 220 |
Number of buttons that Caden had in the end
= 24 u ÷ 2
= 12 u
Number of buttons that Caden sold to Zeph
= 32 u - 12 u
= 20 u
20 u = 220
1 u = 220 ÷ 20 = 11
Number of buttons that Zeph had in the end
= 3 u + 220
= 3 x 11 + 220
= 33 + 220
= 253
Answer(s): 253
