Bottle T contains only 50-cent coins and Bottle U contains only 5-cent coins. There are 14 more coins in Bottle U than in Bottle T. The amount of money in Bottle T is $2.45 more than the amount of money in Bottle U. Find the total amount of money in both bottles.
|
Bottle T |
Bottle U |
Number |
1 u |
1 u + 14 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 70 |
$1 = 100¢
$2.45 = 245¢
Total value of 50¢ coins in Bottle T
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle U
= 5(1 u + 14)
= 5 u + 70
The amount of money in Bottle T is $2.45 more than the amount of money in Bottle U. If another 245¢ is added into Bottle U, the total value of coins in Bottle T and Bottle U will be the same.
50 u = 5 u + 70 + 245
50 u - 5 u = 315
45 u = 315
1 u = 315 ÷ 45 = 7
Total amount in both bottles
= 50 u + (5 u + 70)
= 55 u + 70
= (55 x 7) + 70
= 385 + 70
= 455¢
455¢ = $4.55
Answer(s): $4.55