At first, Ethan had thrice as many chocolate bars as Paul. After they each gave away 20 chocolate bars, Ethan had 7 times as many chocolate bars as Paul. How many chocolate bars did they have altogether at first?
| |
Ethan |
Paul |
Difference |
| Before |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
| Change |
- 20 |
- 20 |
|
| After |
7 u |
1 u |
6 u |
Since they both gave away the same number of chocolate bars, their difference in the number of chocolate bars remains the same. Make the difference in the number of chocolate bars the same. LCM of 2 and 6 is 6.
Number of chocolate bars that each gave away
= 9 u - 7 u
= 2 u
2 u = 20
1 u = 20 ÷ 2 = 10
Number of chocolate bars that they had altogether at first
= 9 u + 3 u
= 12 u
= 12 x 10
= 120
Answer(s): 120
