Bottle D contains only 50-cent coins and Bottle E contains only 5-cent coins. There are 22 more coins in Bottle E than in Bottle D. The amount of money in Bottle D is $1.60 more than the amount of money in Bottle E. Find the total amount of money in both bottles.
| |
Bottle D |
Bottle E |
| Number |
1 u |
1 u + 22 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 110 |
$1 = 100¢
$1.60 = 160¢
Total value of 50¢ coins in Bottle D
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle E
= 5(1 u + 22)
= 5 u + 110
The amount of money in Bottle D is $1.60 more than the amount of money in Bottle E. If another 160¢ is added into Bottle E, the total value of coins in Bottle D and Bottle E will be the same.
50 u = 5 u + 110 + 160
50 u - 5 u = 270
45 u = 270
1 u = 270 ÷ 45 = 6
Total amount in both bottles
= 50 u + (5 u + 110)
= 55 u + 110
= (55 x 6) + 110
= 330 + 110
= 440¢
440¢ = $4.40
Answer(s): $4.40
