Bottle K contains only 50-cent coins and Bottle L contains only 5-cent coins. There are 23 more coins in Bottle L than in Bottle K. The amount of money in Bottle K is $1.55 more than the amount of money in Bottle L. Find the total amount of money in both bottles.
| |
Bottle K |
Bottle L |
| Number |
1 u |
1 u + 23 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 115 |
$1 = 100¢
$1.55 = 155¢
Total value of 50¢ coins in Bottle K
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle L
= 5(1 u + 23)
= 5 u + 115
The amount of money in Bottle K is $1.55 more than the amount of money in Bottle L. If another 155¢ is added into Bottle L, the total value of coins in Bottle K and Bottle L will be the same.
50 u = 5 u + 115 + 155
50 u - 5 u = 270
45 u = 270
1 u = 270 ÷ 45 = 6
Total amount in both bottles
= 50 u + (5 u + 115)
= 55 u + 115
= (55 x 6) + 115
= 330 + 115
= 445¢
445¢ = $4.45
Answer(s): $4.45
