Ethan had twice as many marbles as Bobby. After Bobby lost 12 marbles and Ethan bought 12 marbles, Ethan had 4 times as many marbles as Bobby. How many marbles did Ethan and Bobby have altogether at first?
| |
Ethan |
Bobby |
Total |
| Before |
2x5 =
10 u |
1x5 =
5 u |
3x5 =
15 u |
| Change |
+ 12 |
- 12 |
|
| After |
4x3 =
12 u |
1x3 =
3 u |
5x3 =
15 u |
The number of marbles that Bobby lost and bought is the same. So, the total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 5 is 15.
Number of marbles that Ethan bought
= 12 u - 10 u
= 2 u
2 u = 12
1 u = 12 ÷ 2 = 6
Number of cards that they had altogether at first
= 15 u
= 15 x 6
= 90
Answer(s): 90
