Francois is rolling coins. He has 3 rolls of 40 quarters. He has 8 rolls of 50 dimes. He exchanges 2 rolls of dimes for 1 roll of quarters. How many coins, c, does Francois have?
After the exchange, he has 4 rolls of 40 quarters and 6 rolls of 50 dimes. Work it from there.
Thanks
First, we need to find the total number of quarters that Francois has. Each roll of quarters contains 40 quarters, so the total number of quarters from the rolls of quarters is 3 x 40 = 120 quarters.
Next, we need to find the total number of dimes that Francois has. Each roll of dimes contains 50 dimes, so the total number of dimes from the rolls of dimes is 8 x 50 = 400 dimes.
Since Francois exchanges 2 rolls of dimes for 1 roll of quarters, he exchanges 2 x 50 = 100 dimes for 1 x 40 = 40 quarters.
After the exchange, Francois has 120 + 40 = <<120+40=160>>160 quarters.
Finally, we need to find the total number of coins, c, that Francois has. Francois has 160 quarters and 400 dimes, so the total number of coins is 160 + 400 = <<160+400=560>>560 coins.
Therefore, Francois has a total of 560 coins.
To find the total number of coins that Francois has, we need to calculate the number of quarters and dimes separately and then add them together.
Francois has 3 rolls of 40 quarters, so the number of quarters he has can be calculated by multiplying the number of rolls by the number of quarters in each roll:
Number of quarters = 3 rolls * 40 quarters/roll = 120 quarters
Similarly, Francois has 8 rolls of 50 dimes, so the number of dimes he has can be calculated by multiplying the number of rolls by the number of dimes in each roll:
Number of dimes = 8 rolls * 50 dimes/roll = 400 dimes
Next, we need to determine how many rolls of dimes can be exchanged for a roll of quarters. Given that 2 rolls of dimes can be exchanged for 1 roll of quarters, we can convert some of the dimes into quarters.
Since Francois wants to exchange 2 rolls of dimes, we divide the number of rolls of dimes by 2 to find out how many rolls of quarters he can obtain:
Number of rolls of quarters = 8 rolls of dimes / 2 = 4 rolls of quarters
Now, we can add the number of quarters and the number of quarters obtained from the exchange together to find the total number of quarters Francois has:
Total number of quarters = 120 quarters + 4 rolls of quarters * 40 quarters/roll = 280 quarters
Finally, we add the number of quarters and the number of dimes to find the total number of coins:
Total number of coins = Total number of quarters + Number of dimes
Total number of coins = 280 quarters + 400 dimes = 680 coins
Therefore, Francois has a total of 680 coins.