Pouch R contains only 50-cent coins and Pouch S contains only 5-cent coins. There are 10 more coins in Pouch S than in Pouch R. The amount of money in Pouch R is $3.10 more than the amount of money in Pouch S. Find the total amount of money in both pouches.
| |
Pouch R |
Pouch S |
| Number |
1 u |
1 u + 10 |
| Value |
50¢ |
5¢ |
| Total value |
50 u |
5 u + 50 |
$1 = 100¢
$3.10 = 310¢
Total value of 50¢ coins in Pouch R
= 50 x 1 u
= 50 u
Total value of 5¢ coins in Pouch S
= 5(1 u + 10)
= 5 u + 50
The amount of money in Pouch R is $3.10 more than the amount of money in Pouch S. If another 310¢ is added into Pouch S, the total value of coins in Pouch R and Pouch S will be the same.
50 u = 5 u + 50 + 310
50 u - 5 u = 360
45 u = 360
1 u = 360 ÷ 45 = 8
Total amount in both pouches
= 50 u + (5 u + 50)
= 55 u + 50
= (55 x 8) + 50
= 440 + 50
= 490¢
490¢ = $4.90
Answer(s): $4.90
