Bag P contains only 50-cent coins and Bag Q contains only 5-cent coins. There are 13 more coins in Bag Q than in Bag P. The amount of money in Bag P is $2.50 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 + 13 |
Value |
50¢ |
5¢ |
Total value |
50 u |
5 u + 65 |
$1 = 100¢
$2.50 = 250¢
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 + 13)
= 5 u + 65
The amount of money in Bag P is $2.50 more than the amount of money in Bag Q. If another 250¢ is added into Bag Q, the total value of coins in Bag P and Bag Q 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 bags
= 50 u + (5 u + 65)
= 55 u + 65
= (55 x 7) + 65
= 385 + 65
= 450¢
450¢ = $4.50
Answer(s): $4.50