Bottle A contains only 50-cent coins and Bottle B contains only 5-cent coins. There are 24 more coins in Bottle B than in Bottle A. The amount of money in Bottle A is $2.40 more than the amount of money in Bottle B. Find the total amount of money in both bottles.
| |
Bottle A |
Bottle B |
| Number |
1 u |
1 u + 24 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 120 |
$1 = 100¢
$2.40 = 240¢
Total value of 50¢ coins in Bottle A
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle B
= 5(1 u + 24)
= 5 u + 120
The amount of money in Bottle A is $2.40 more than the amount of money in Bottle B. If another 240¢ is added into Bottle B, the total value of coins in Bottle A and Bottle B will be the same.
50 u = 5 u + 120 + 240
50 u - 5 u = 360
45 u = 360
1 u = 360 ÷ 45 = 8
Total amount in both bottles
= 50 u + (5 u + 120)
= 55 u + 120
= (55 x 8) + 120
= 440 + 120
= 560¢
560¢ = $5.60
Answer(s): $5.60
