Coin Box T contains only 50-cent coins and Coin Box U contains only 5-cent coins. There are 23 more coins in Coin Box U than in Coin Box T. The amount of money in Coin Box T is $2.90 more than the amount of money in Coin Box U. Find the total amount of money in both coin boxes.
|
Coin Box T |
Coin Box U |
Number |
1 u |
1 u + 23 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 115 |
$1 = 100¢
$2.90 = 290¢
Total value of 50¢ coins in Coin Box T
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Coin Box U
= 5(1 u + 23)
= 5 u + 115
The amount of money in Coin Box T is $2.90 more than the amount of money in Coin Box U. If another 290¢ is added into Coin Box U, the total value of coins in Coin Box T and Coin Box U will be the same.
50 u = 5 u + 115 + 290
50 u - 5 u = 405
45 u = 405
1 u = 405 ÷ 45 = 9
Total amount in both coin boxes
= 50 u + (5 u + 115)
= 55 u + 115
= (55 x 9) + 115
= 495 + 115
= 610¢
610¢ = $6.10
Answer(s): $6.10