Bag X contains only 50-cent coins and Bag Y contains only 5-cent coins. There are 24 more coins in Bag Y than in Bag X. The amount of money in Bag X is $1.50 more than the amount of money in Bag Y. Find the total amount of money in both bags.
| |
Bag X |
Bag Y |
| Number |
1 u |
1 u + 24 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 120 |
$1 = 100¢
$1.50 = 150¢
Total value of 50¢ coins in Bag X
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag Y
= 5(1 u + 24)
= 5 u + 120
The amount of money in Bag X is $1.50 more than the amount of money in Bag Y. If another 150¢ is added into Bag Y, the total value of coins in Bag X and Bag Y will be the same.
50 u = 5 u + 120 + 150
50 u - 5 u = 270
45 u = 270
1 u = 270 ÷ 45 = 6
Total amount in both bags
= 50 u + (5 u + 120)
= 55 u + 120
= (55 x 6) + 120
= 330 + 120
= 450¢
450¢ = $4.50
Answer(s): $4.50
