Bottle G contains only 50-cent coins and Bottle H contains only 10-cent coins. There are 23 more coins in Bottle H than in Bottle G. The amount of money in Bottle G is $1.70 more than the amount of money in Bottle H. Find the total amount of money in both bottles.
| |
Bottle G |
Bottle H |
| Number |
1 u |
1 u + 23 |
| Value |
50¢ |
10¢ |
| Total value |
50 u |
10 u + 230 |
$1 = 100¢
$1.70 = 170¢
Total value of 50¢ coins in Bottle G
= 50 x 1 u
= 50 u
Total value of 10¢ coins in Bottle H
= 10(1 u + 23)
= 10 u + 230
The amount of money in Bottle G is $1.70 more than the amount of money in Bottle H. If another 170¢ is added into Bottle H, the total value of coins in Bottle G and Bottle H will be the same.
50 u = 10 u + 230 + 170
50 u - 10 u = 400
40 u = 400
1 u = 400 ÷ 40 = 10
Total amount in both bottles
= 50 u + (10 u + 230)
= 60 u + 230
= (60 x 10) + 230
= 600 + 230
= 830¢
830¢ = $8.30
Answer(s): $8.30
