Pouch J contains 50-cent coins and Pouch K contains 20-cent coins. There are 11 more coins in Pouch K than in Pouch J. The amount of money in Pouch J is 410¢ more than the amount of money in Pouch K. How many total coins are there?
| |
Pouch J |
Pouch K |
| Number |
1 u |
1 u + 11 |
| Value |
50¢ |
20¢ |
| Total value |
50 u |
20 u + 220 |
Total value of 50¢ coins in Pouch J
= 50 x 1 u
= 50 u
Total value of 20¢ coins in Pouch K
= 20 x (1 u + 11)
= 20 u + 220
The amount in Pouch J is 410¢ more than Pouch K. If another 410¢ is added into Pouch K, both Pouch J and Pouch K will have the same amounts of money.
50 u = 20 u + 220 + 410
50 u - 20 u = 220 + 410
30 u = 630
1 u = 630 ÷ 30 = 21
Total number of coins
= 1 u + (1 u + 11)
= 2 u + 11
= 2 x 21 + 11
= 42 + 11
= 53
Answer(s): 53
