Bottle U contains only 50-cent coins and Bottle V contains only 10-cent coins. There are 11 more coins in Bottle V than in Bottle U. The amount of money in Bottle U is $2.50 more than the amount of money in Bottle V. Find the total amount of money in both bottles.
| |
Bottle U |
Bottle V |
| Number |
1 u |
1 u + 11 |
| Value |
50¢ |
10¢ |
| Total value |
50 u |
10 u + 110 |
$1 = 100¢
$2.50 = 250¢
Total value of 50¢ coins in Bottle U
= 50 x 1 u
= 50 u
Total value of 10¢ coins in Bottle V
= 10(1 u + 11)
= 10 u + 110
The amount of money in Bottle U is $2.50 more than the amount of money in Bottle V. If another 250¢ is added into Bottle V, the total value of coins in Bottle U and Bottle V will be the same.
50 u = 10 u + 110 + 250
50 u - 10 u = 360
40 u = 360
1 u = 360 ÷ 40 = 9
Total amount in both bottles
= 50 u + (10 u + 110)
= 60 u + 110
= (60 x 9) + 110
= 540 + 110
= 650¢
650¢ = $6.50
Answer(s): $6.50
