Lucy had 120 more buttons than Gem. After Lucy gave away
15 of her buttons and Gem gave away
13 of her buttons, Gem had 106 less buttons than Lucy. How many buttons did Lucy have at first?
| |
Lucy |
Gem |
Comparing Lucy and
Gem at first |
120 more |
|
| Before |
5x3 |
+ 120 |
3x5 |
| Change |
- 1x3 |
- 24 |
- 1x5 |
| After |
4x3 |
+ 96 |
2x5 |
Comparing Lucy and
Gem in the end |
|
106 less |
| |
Lucy |
Gem |
| Before |
15 u + 120 |
15 u |
| Change |
- 3 u - 24 |
- 5 u |
| After |
12 u + 96 |
10 u |
15 x 120 = 24
120 - 24 = 96
Gem had 106 less buttons than Lucy in the end. So, if Gem had another 106 buttons in the end, the number of buttons that Gem and Lucy each had would be the same.
12 u + 96 = 10 u + 106
12 u - 10 u = 106 - 96
2 u = 10
1 u = 10 ÷ 2 = 5
Number of buttons that Lucy had at first
= 15 u + 120
= 15 x 5 + 120
= 75 + 120
= 195
Answer(s): 195
