Pouch Y contains only 50-cent coins and Pouch Z contains only 10-cent coins. There are 22 more coins in Pouch Z than in Pouch Y. The amount of money in Pouch Y is $1.80 more than the amount of money in Pouch Z. Find the total amount of money in both pouches.
| |
Pouch Y |
Pouch Z |
| Number |
1 u |
1 u + 22 |
| Value |
50¢ |
10¢ |
| Total value |
50 u |
10 u + 220 |
$1 = 100¢
$1.80 = 180¢
Total value of 50¢ coins in Pouch Y
= 50 x 1 u
= 50 u
Total value of 10¢ coins in Pouch Z
= 10(1 u + 22)
= 10 u + 220
The amount of money in Pouch Y is $1.80 more than the amount of money in Pouch Z. If another 180¢ is added into Pouch Z, the total value of coins in Pouch Y and Pouch Z will be the same.
50 u = 10 u + 220 + 180
50 u - 10 u = 400
40 u = 400
1 u = 400 ÷ 40 = 10
Total amount in both pouches
= 50 u + (10 u + 220)
= 60 u + 220
= (60 x 10) + 220
= 600 + 220
= 820¢
820¢ = $8.20
Answer(s): $8.20
