Jar J contains only 50-cent coins and Jar K contains only 5-cent coins. There are 18 more coins in Jar K than in Jar J. The amount of money in Jar J is $2.70 more than the amount of money in Jar K. Find the total amount of money in both jars.
| |
Jar J |
Jar K |
| Number |
1 u |
1 u + 18 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 90 |
$1 = 100¢
$2.70 = 270¢
Total value of 50¢ coins in Jar J
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Jar K
= 5(1 u + 18)
= 5 u + 90
The amount of money in Jar J is $2.70 more than the amount of money in Jar K. If another 270¢ is added into Jar K, the total value of coins in Jar J and Jar K will be the same.
50 u = 5 u + 90 + 270
50 u - 5 u = 360
45 u = 360
1 u = 360 ÷ 45 = 8
Total amount in both jars
= 50 u + (5 u + 90)
= 55 u + 90
= (55 x 8) + 90
= 440 + 90
= 530¢
530¢ = $5.30
Answer(s): $5.30
