Bottle S contains only 50-cent coins and Bottle T contains only 5-cent coins. There are 13 more coins in Bottle T than in Bottle S. The amount of money in Bottle S is $2.50 more than the amount of money in Bottle T. Find the total amount of money in both bottles.
| |
Bottle S |
Bottle T |
| Number |
1 u |
1 u + 13 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 65 |
$1 = 100¢
$2.50 = 250¢
Total value of 50¢ coins in Bottle S
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bottle T
= 5(1 u + 13)
= 5 u + 65
The amount of money in Bottle S is $2.50 more than the amount of money in Bottle T. If another 250¢ is added into Bottle T, the total value of coins in Bottle S and Bottle T will be the same.
50 u = 5 u + 65 + 250
50 u - 5 u = 315
45 u = 315
1 u = 315 ÷ 45 = 7
Total amount in both bottles
= 50 u + (5 u + 65)
= 55 u + 65
= (55 x 7) + 65
= 385 + 65
= 450¢
450¢ = $4.50
Answer(s): $4.50
