Bag Y contains only 50-cent coins and Bag Z contains only 5-cent coins. There are 19 more coins in Bag Z than in Bag Y. The amount of money in Bag Y is $3.10 more than the amount of money in Bag Z. Find the total amount of money in both bags.
| |
Bag Y |
Bag Z |
| Number |
1 u |
1 u + 19 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 95 |
$1 = 100¢
$3.10 = 310¢
Total value of 50¢ coins in Bag Y
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Bag Z
= 5(1 u + 19)
= 5 u + 95
The amount of money in Bag Y is $3.10 more than the amount of money in Bag Z. If another 310¢ is added into Bag Z, the total value of coins in Bag Y and Bag Z will be the same.
50 u = 5 u + 95 + 310
50 u - 5 u = 405
45 u = 405
1 u = 405 ÷ 45 = 9
Total amount in both bags
= 50 u + (5 u + 95)
= 55 u + 95
= (55 x 9) + 95
= 495 + 95
= 590¢
590¢ = $5.90
Answer(s): $5.90
