Caden and Howard had some erasers in the ratio of 8 : 7. Howard and Simon had some erasers in the ratio of 4 : 1. Caden sold 180 erasers to Simon and ended up with half the number of erasers Howard had. How many erasers did Simon have in the end?
| Caden |
Howard |
Simon |
| 8x4 |
7x4 |
|
| |
4x7 |
1x7 |
| 32 u |
28 u |
7 u |
The number of erasers that Howard had at first is repeated. Make the number of erasers that Howard had at first the same. LCM of 7 and 4 is 28.
| |
Caden |
Howard |
Simon |
| Before |
32 u |
28 u |
7 u |
| Change |
- 180 |
|
+ 180 |
| After |
14 u |
28 u |
7 u + 180 |
Number of erasers that Caden had in the end
= 28 u ÷ 2
= 14 u
Number of erasers that Caden sold to Simon
= 32 u - 14 u
= 18 u
18 u = 180
1 u = 180 ÷ 18 = 10
Number of erasers that Simon had in the end
= 7 u + 180
= 7 x 10 + 180
= 70 + 180
= 250
Answer(s): 250
