Bottle J contains only 50-cent coins and Bottle K contains only 5-cent coins. There are 19 more coins in Bottle K than in Bottle J. The amount of money in Bottle J is $2.20 more than the amount of money in Bottle K. Find the total amount of money in both bottles.
| |
Bottle J |
Bottle K |
| Number |
1 u |
1 u + 19 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 95 |
$1 = 100¢
$2.20 = 220¢
Total value of 50¢ coins in Bottle J
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle K
= 5(1 u + 19)
= 5 u + 95
The amount of money in Bottle J is $2.20 more than the amount of money in Bottle K. If another 220¢ is added into Bottle K, the total value of coins in Bottle J and Bottle K will be the same.
50 u = 5 u + 95 + 220
50 u - 5 u = 315
45 u = 315
1 u = 315 ÷ 45 = 7
Total amount in both bottles
= 50 u + (5 u + 95)
= 55 u + 95
= (55 x 7) + 95
= 385 + 95
= 480¢
480¢ = $4.80
Answer(s): $4.80
