Pouch J contains 50-cent coins and Pouch K contains 5-cent coins. There are 34 more coins in Pouch K than in Pouch J. The amount of money in Pouch J is 865¢ more than the amount of money in Pouch K. How many total coins are there?
|
Pouch J |
Pouch K |
Number |
1 u |
1 u + 34 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 170 |
Total value of 50¢ coins in Pouch J
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Pouch K
= 5 x (1 u + 34)
= 5 u + 170
The amount in Pouch J is 865¢ more than Pouch K. If another 865¢ is added into Pouch K, both Pouch J and Pouch K will have the same amounts of money.
50 u = 5 u + 170 + 865
50 u - 5 u = 170 + 865
45 u = 1035
1 u = 1035 ÷ 45 = 23
Total number of coins
= 1 u + (1 u + 34)
= 2 u + 34
= 2 x 23 + 34
= 46 + 34
= 80
Answer(s): 80