Bag T contains only 50-cent coins and Bag U contains only 5-cent coins. There are 20 more coins in Bag U than in Bag T. The amount of money in Bag T is $2.60 more than the amount of money in Bag U. Find the total amount of money in both bags.
| |
Bag T |
Bag U |
| Number |
1 u |
1 u + 20 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 100 |
$1 = 100¢
$2.60 = 260¢
Total value of 50¢ coins in Bag T
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag U
= 5(1 u + 20)
= 5 u + 100
The amount of money in Bag T is $2.60 more than the amount of money in Bag U. If another 260¢ is added into Bag U, the total value of coins in Bag T and Bag U will be the same.
50 u = 5 u + 100 + 260
50 u - 5 u = 360
45 u = 360
1 u = 360 ÷ 45 = 8
Total amount in both bags
= 50 u + (5 u + 100)
= 55 u + 100
= (55 x 8) + 100
= 440 + 100
= 540¢
540¢ = $5.40
Answer(s): $5.40
