Bottle M contains 20-cent coins and Bottle N contains 5-cent coins. There are 31 more coins in Bottle N than in Bottle M. The amount of money in Bottle M is 160¢ more than the amount of money in Bottle N. How many total coins are there?
| |
Bottle M |
Bottle N |
| Number |
1 u |
1 u + 31 |
| Value |
20¢ |
5¢ |
| Total value |
20 u |
5 u + 155 |
Total value of 20¢ coins in Bottle M
= 20 x 1 u
= 20 u
Total value of 5¢ coins in Bottle N
= 5 x (1 u + 31)
= 5 u + 155
The amount in Bottle M is 160¢ more than Bottle N. If another 160¢ is added into Bottle N, both Bottle M and Bottle N will have the same amounts of money.
20 u = 5 u + 155 + 160
20 u - 5 u = 155 + 160
15 u = 315
1 u = 315 ÷ 15 = 21
Total number of coins
= 1 u + (1 u + 31)
= 2 u + 31
= 2 x 21 + 31
= 42 + 31
= 73
Answer(s): 73
