SOLUTION: a. State sales tax S is directly proportional to retail price p . An item that sells for 180 dollars has a sales tax of 10.22 dollars. Find a mathematical model that gives the

Question 1171022: a. State sales tax S is directly proportional to retail price p . An item that sells for 180 dollars has a sales tax of 10.22 dollars.
Find a mathematical model that gives the amount of sales tax S in terms of the retail price p .
Function:S(p)=
b. What is the sales tax on a 350 dollars purchase. Round to the nearest cent.
The sales tax on a 350 dollar purchase is $
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

a. State sales tax S is directly proportional to retail price p . An item that sells for 180 dollars has a sales tax of 10.22 dollars.
Find a mathematical model that gives the amount of sales tax S in terms of the retail price p .
Function:S(p)=
b. What is the sales tax on a 350 dollars purchase. Round to the nearest cent.
The sales tax on a 350 dollar purchase is $

Correct answer:
Substitute $350 for p in the above function, and you should get a correct answer of:
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