Jen had 105 more buttons than Esther. After Jen gave away
13 of her buttons and Esther gave away
34 of her buttons, Esther had 120 less buttons than Jen. How many buttons did Jen have at first?
| |
Jen |
Esther |
Comparing Jen and
Esther at first |
105 more |
|
| Before |
3x4 |
+ 105 |
4x3 |
| Change |
- 1x4 |
- 35 |
- 3x3 |
| After |
2x4 |
+ 70 |
1x3 |
Comparing Jen and
Esther in the end |
|
120 less |
| |
Jen |
Esther |
| Before |
12 u + 105 |
12 u |
| Change |
- 4 u - 35 |
- 9 u |
| After |
8 u + 70 |
3 u |
13 x 105 = 35
105 - 35 = 70
Esther had 120 less buttons than Jen in the end. So, if Esther had another 120 buttons in the end, the number of buttons that Esther and Jen each had would be the same.
8 u + 70 = 3 u + 120
8 u - 3 u = 120 - 70
5 u = 50
1 u = 50 ÷ 5 = 10
Number of buttons that Jen had at first
= 12 u + 105
= 12 x 10 + 105
= 120 + 105
= 225
Answer(s): 225
