Bag U contains only 50-cent coins and Bag V contains only 5-cent coins. There are 24 more coins in Bag V than in Bag U. The amount of money in Bag U is $1.05 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 + 24 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 120 |
$1 = 100¢
$1.05 = 105¢
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 + 24)
= 5 u + 120
The amount of money in Bag U is $1.05 more than the amount of money in Bag V. If another 105¢ is added into Bag V, the total value of coins in Bag U and Bag V will be the same.
50 u = 5 u + 120 + 105
50 u - 5 u = 225
45 u = 225
1 u = 225 ÷ 45 = 5
Total amount in both bags
= 50 u + (5 u + 120)
= 55 u + 120
= (55 x 5) + 120
= 275 + 120
= 395¢
395¢ = $3.95
Answer(s): $3.95
