Pouch X contains 50-cent coins and Pouch Y contains 5-cent coins. There are 21 more coins in Pouch Y than in Pouch X. The amount of money in Pouch X is 1065¢ more than the amount of money in Pouch Y. How many total coins are there?
| |
Pouch X |
Pouch Y |
| Number |
1 u |
1 u + 21 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 105 |
Total value of 50¢ coins in Pouch X
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Pouch Y
= 5 x (1 u + 21)
= 5 u + 105
The amount in Pouch X is 1065¢ more than Pouch Y. If another 1065¢ is added into Pouch Y, both Pouch X and Pouch Y will have the same amounts of money.
50 u = 5 u + 105 + 1065
50 u - 5 u = 105 + 1065
45 u = 1170
1 u = 1170 ÷ 45 = 26
Total number of coins
= 1 u + (1 u + 21)
= 2 u + 21
= 2 x 26 + 21
= 52 + 21
= 73
Answer(s): 73
