Bag X contains only 50-cent coins and Bag Y contains only 5-cent coins. There are 20 more coins in Bag Y than in Bag X. The amount of money in Bag X is $3.50 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 + 20 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 100 |
$1 = 100¢
$3.50 = 350¢
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 + 20)
= 5 u + 100
The amount of money in Bag X is $3.50 more than the amount of money in Bag Y. If another 350¢ is added into Bag Y, the total value of coins in Bag X and Bag Y will be the same.
50 u = 5 u + 100 + 350
50 u - 5 u = 450
45 u = 450
1 u = 450 ÷ 45 = 10
Total amount in both bags
= 50 u + (5 u + 100)
= 55 u + 100
= (55 x 10) + 100
= 550 + 100
= 650¢
650¢ = $6.50
Answer(s): $6.50