At first, Archie had twice as many candy canes as Seth. After they each gave away 15 candy canes, Archie had 7 times as many candy canes as Seth. How many candy canes did they have altogether at first?
| |
Archie |
Seth |
Difference |
| Before |
2x6 =
12 u |
1x6 =
6 u |
1x6 =
6 u |
| Change |
- 15 |
- 15 |
|
| After |
7 u |
1 u |
6 u |
Since they both gave away the same number of candy canes, their difference in the number of candy canes remains the same. Make the difference in the number of candy canes the same. LCM of 1 and 6 is 6.
Number of candy canes that each gave away
= 12 u - 7 u
= 5 u
5 u = 15
1 u = 15 ÷ 5 = 3
Number of candy canes that they had altogether at first
= 12 u + 6 u
= 18 u
= 18 x 3
= 54
Answer(s): 54
