Bag P contains only 50-cent coins and Bag Q contains only 10-cent coins. There are 10 more coins in Bag Q than in Bag P. The amount of money in Bag P is $2.60 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 + 10 |
| Value |
50¢ |
10¢ |
| Total value |
50 u |
10 u + 100 |
$1 = 100¢
$2.60 = 260¢
Total value of 50¢ coins in Bag P
= 50 x 1 u
= 50 u
Total value of 10¢ coins in Bag Q
= 10(1 u + 10)
= 10 u + 100
The amount of money in Bag P is $2.60 more than the amount of money in Bag Q. If another 260¢ is added into Bag Q, the total value of coins in Bag P and Bag Q will be the same.
50 u = 10 u + 100 + 260
50 u - 10 u = 360
40 u = 360
1 u = 360 ÷ 40 = 9
Total amount in both bags
= 50 u + (10 u + 100)
= 60 u + 100
= (60 x 9) + 100
= 540 + 100
= 640¢
640¢ = $6.40
Answer(s): $6.40
