Pouch K contains 20-cent coins and Pouch L contains 5-cent coins. There are 27 more coins in Pouch L than in Pouch K. The amount of money in Pouch K is 75¢ more than the amount of money in Pouch L. How many total coins are there?
| |
Pouch K |
Pouch L |
| Number |
1 u |
1 u + 27 |
| Value |
20¢ |
5¢ |
| Total value |
20 u |
5 u + 135 |
Total value of 20¢ coins in Pouch K
= 20 x 1 u
= 20 u
Total value of 5¢ coins in Pouch L
= 5 x (1 u + 27)
= 5 u + 135
The amount in Pouch K is 75¢ more than Pouch L. If another 75¢ is added into Pouch L, both Pouch K and Pouch L will have the same amounts of money.
20 u = 5 u + 135 + 75
20 u - 5 u = 135 + 75
15 u = 210
1 u = 210 ÷ 15 = 14
Total number of coins
= 1 u + (1 u + 27)
= 2 u + 27
= 2 x 14 + 27
= 28 + 27
= 55
Answer(s): 55
