Betty had the same number of yellow, gold and purple coins at first. After giving some yellow and gold coins and 57 purple coins away, Betty had 219 coins left. There were 5 times as many yellow coins as gold coins left. The number of purple coins left was 45 fewer than the number of yellow coins left. How many purple coins did she have at first?
| |
Gold |
Yellow |
Purple |
Total |
| Before |
5 u + 12 |
5 u + 12 |
5 u + 12 |
|
| Change |
- 4 u - 12 |
- 12 |
- 57 |
|
| After |
1 u |
5 u |
5 u - 45 |
219 |
Betty had the same number of yellow, gold and purple coins at first.
Total number of coins in the end
= 1 u + 5 u + 5 u - 45
= 11 u - 45
11 u - 45 = 219
11 u = 219 + 45
11 u = 264
1 u = 264 ÷ 11 = 24
Number of purple coins that Betty had at first
= 5 u - 45 + 57
= 5 u + 12
= 5 x 24 + 12
= 132
Answer(s): 132
