Bag P contains only 50-cent coins and Bag Q contains only 5-cent coins. There are 22 more coins in Bag Q than in Bag P. The amount of money in Bag P is $2.05 more than the amount of money in Bag Q. Find the total amount of money in both bags.
| |
Bag P |
Bag Q |
| Number |
1 u |
1 u + 22 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 110 |
$1 = 100¢
$2.05 = 205¢
Total value of 50¢ coins in Bag P
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag Q
= 5(1 u + 22)
= 5 u + 110
The amount of money in Bag P is $2.05 more than the amount of money in Bag Q. If another 205¢ is added into Bag Q, the total value of coins in Bag P and Bag Q will be the same.
50 u = 5 u + 110 + 205
50 u - 5 u = 315
45 u = 315
1 u = 315 ÷ 45 = 7
Total amount in both bags
= 50 u + (5 u + 110)
= 55 u + 110
= (55 x 7) + 110
= 385 + 110
= 495¢
495¢ = $4.95
Answer(s): $4.95
