Bag J contains only 50-cent coins and Bag K contains only 10-cent coins. There are 11 more coins in Bag K than in Bag J. The amount of money in Bag J is $2.10 more than the amount of money in Bag K. Find the total amount of money in both bags.
| |
Bag J |
Bag K |
| Number |
1 u |
1 u + 11 |
| Value |
50¢ |
10¢ |
| Total value |
50 u |
10 u + 110 |
$1 = 100¢
$2.10 = 210¢
Total value of 50¢ coins in Bag J
= 50 x 1 u
= 50 u
Total value of 10¢ coins in Bag K
= 10(1 u + 11)
= 10 u + 110
The amount of money in Bag J is $2.10 more than the amount of money in Bag K. If another 210¢ is added into Bag K, the total value of coins in Bag J and Bag K will be the same.
50 u = 10 u + 110 + 210
50 u - 10 u = 320
40 u = 320
1 u = 320 ÷ 40 = 8
Total amount in both bags
= 50 u + (10 u + 110)
= 60 u + 110
= (60 x 8) + 110
= 480 + 110
= 590¢
590¢ = $5.90
Answer(s): $5.90
