Bottle X contains only 50-cent coins and Bottle Y contains only 5-cent coins. There are 17 more coins in Bottle Y than in Bottle X. The amount of money in Bottle X is $2.30 more than the amount of money in Bottle Y. Find the total amount of money in both bottles.
|
Bottle X |
Bottle Y |
Number |
1 u |
1 u + 17 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 85 |
$1 = 100¢
$2.30 = 230¢
Total value of 50¢ coins in Bottle X
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle Y
= 5(1 u + 17)
= 5 u + 85
The amount of money in Bottle X is $2.30 more than the amount of money in Bottle Y. If another 230¢ is added into Bottle Y, the total value of coins in Bottle X and Bottle Y will be the same.
50 u = 5 u + 85 + 230
50 u - 5 u = 315
45 u = 315
1 u = 315 ÷ 45 = 7
Total amount in both bottles
= 50 u + (5 u + 85)
= 55 u + 85
= (55 x 7) + 85
= 385 + 85
= 470¢
470¢ = $4.70
Answer(s): $4.70