Question 1171022
an item that sells for 180 has a sales tax of 10.22.
the tax rate is therefore 10.22 / 180.
the function is s(p) = 10.22/180 * p


when p = 350, s(p) = 10.22/180 * 350 = 19.8722222222.


since they are directly proportional, 10.22/180 = 19.8722222222/350.
cross multiply to get:
10.22*350 = 19.8722222222*180 resulting in:
3577 = 3577
this confirms the ratio is correct.


if you were to use the direct proportion formula of y = k * x, then you would have done the following.


when x = 180 and y = 10.22, the formula becomes:
10.22 = 180 * k
solve for k to get:
k = 10.22/180.
k is the constant of variation.


when x = 350, y = k * x becomes y = 10.22/180 * 350 = 19.8722222222.
tax on 180 is 10.22.
tax on 350 is 19.8722222222.
the numbers are rounded to 8 repeating decimals.


you solution is that the tax on 350 dollars purchase is 19.87.