Bottle E contains 20-cent coins and Bottle F contains 5-cent coins. There are 31 more coins in Bottle F than in Bottle E. The amount of money in Bottle E is 160¢ more than the amount of money in Bottle F. How many total coins are there?
| |
Bottle E |
Bottle F |
| Number |
1 u |
1 u + 31 |
| Value |
20¢ |
5¢ |
| Total value |
20 u |
5 u + 155 |
Total value of 20¢ coins in Bottle E
= 20 x 1 u
= 20 u
Total value of 5¢ coins in Bottle F
= 5 x (1 u + 31)
= 5 u + 155
The amount in Bottle E is 160¢ more than Bottle F. If another 160¢ is added into Bottle F, both Bottle E and Bottle F 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
