Bag Q contains only 50-cent coins and Bag R contains only 5-cent coins. There are 15 more coins in Bag R than in Bag Q. The amount of money in Bag Q is $1.05 more than the amount of money in Bag R. Find the total amount of money in both bags.
| |
Bag Q |
Bag R |
| Number |
1 u |
1 u + 15 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 75 |
$1 = 100¢
$1.05 = 105¢
Total value of 50¢ coins in Bag Q
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag R
= 5(1 u + 15)
= 5 u + 75
The amount of money in Bag Q is $1.05 more than the amount of money in Bag R. If another 105¢ is added into Bag R, the total value of coins in Bag Q and Bag R will be the same.
50 u = 5 u + 75 + 105
50 u - 5 u = 180
45 u = 180
1 u = 180 ÷ 45 = 4
Total amount in both bags
= 50 u + (5 u + 75)
= 55 u + 75
= (55 x 4) + 75
= 220 + 75
= 295¢
295¢ = $2.95
Answer(s): $2.95
