Vincent had 9 coins and Dylan had 10 coins. Their coins consisted of twenty-cent coins and fifty-cent coins. When all their fifty-cent coins were exchanged for twenty-cent coins, they had a total of 31 coins. How many twenty-cent coins did they have at first?
|
Twenty-cent coins |
Fifty-cent coins |
Total |
Before |
31 - 5 u |
2 u |
19 |
Change |
+ 5 u |
- 2 u |
+ 3 u |
After |
31 |
0 |
31 |
Number of coins at first
= 9 + 10
= 19
2 fifty-cent coins can be exchanged for 5 twenty-cent coins.
Increase in the number of coins after all the fifty-cent coins were exchanged for twenty-cent coins
= 5 u - 2 u
= 3 u
3 u = 31 - 19
3 u = 12
1 u = 12 ÷ 3 = 4
Number of twenty-cent coins at first
= 31 - 5 u
= 31 - 5 x 4
= 31 - 20
= 11
Answer(s): 11