Bag P contains 20-cent coins and Bag Q contains 5-cent coins. There are 31 more coins in Bag Q than in Bag P. The amount of money in Bag P is 190¢ more than the amount of money in Bag Q. How many total coins are there?
| |
Bag P |
Bag Q |
| Number |
1 u |
1 u + 31 |
| Value |
20¢ |
5¢ |
| Total value |
20 u |
5 u + 155 |
Total value of 20¢ coins in Bag P
= 20 x 1 u
= 20 u
Total value of 5¢ coins in Bag Q
= 5 x (1 u + 31)
= 5 u + 155
The amount in Bag P is 190¢ more than Bag Q. If another 190¢ is added into Bag Q, both Bag P and Bag Q will have the same amounts of money.
20 u = 5 u + 155 + 190
20 u - 5 u = 155 + 190
15 u = 345
1 u = 345 ÷ 15 = 23
Total number of coins
= 1 u + (1 u + 31)
= 2 u + 31
= 2 x 23 + 31
= 46 + 31
= 77
Answer(s): 77
