A group of three friends ate dinner at a restaurant. when they settled the check, peter paid 4/5 as much as john paid, and john paid 1/3 as much as ralph paid. what fraction of the check john pay?
Let's assume Ralph paid x amount for the check.
John paid 1/3 of what Ralph paid, so John paid (1/3)*x = x/3.
Peter paid 4/5 of what John paid, so Peter paid (4/5)*(x/3) = (4/15)*x.
To find the fraction of the check John paid, we need to express John's payment as a fraction of the total check.
The total check amount is x, so John's payment is x/3.
Therefore, the fraction of the check John paid is (x/3)/x.
Simplifying this fraction, we get (x/3)*(1/x) = 1/3.
So, John paid 1/3 of the check.
Let's assume that Ralph paid the total amount as 1 unit.
John paid 1/3 as much as Ralph, so John paid (1/3) * 1 = 1/3 units.
Peter paid 4/5 as much as John, so Peter paid (4/5) * (1/3) = 4/15 units.
Therefore, John paid a fraction of the check equal to 1/3.