Bag U contains only 50-cent coins and Bag V contains only 5-cent coins. There are 17 more coins in Bag V than in Bag U. The amount of money in Bag U is $2.75 more than the amount of money in Bag V. Find the total amount of money in both bags.
|
Bag U |
Bag V |
Number |
1 u |
1 u + 17 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 85 |
$1 = 100¢
$2.75 = 275¢
Total value of 50¢ coins in Bag U
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag V
= 5(1 u + 17)
= 5 u + 85
The amount of money in Bag U is $2.75 more than the amount of money in Bag V. If another 275¢ is added into Bag V, the total value of coins in Bag U and Bag V will be the same.
50 u = 5 u + 85 + 275
50 u - 5 u = 360
45 u = 360
1 u = 360 ÷ 45 = 8
Total amount in both bags
= 50 u + (5 u + 85)
= 55 u + 85
= (55 x 8) + 85
= 440 + 85
= 525¢
525¢ = $5.25
Answer(s): $5.25