State sales tax is based on retail price. An item that sells for $115.99 has a sales tax of $8.12. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x. (Round the coefficient to two decimal places.)
y =
Use the model to find the sales tax on a $530.50 purchase. (Round your answer to the nearest cent.)
$
rate = 8.12/115.99 = .070006035
but since the $8.12 was most likely rounded off to the nearest cent, I would say it was .07 or 7%
so y = .07x
so when x = 530.50
y = .07(530.50) = $37.14
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To find the mathematical model that gives the amount of sales tax y in terms of the retail price x, we first need to determine the relationship between the two variables.
From the given information, we know that an item that sells for $115.99 has a sales tax of $8.12. This means that the sales tax is a certain percentage of the retail price.
Let's consider the sales tax as a percentage of the retail price. We can represent this percentage as a decimal value, t.
Therefore, the amount of sales tax y can be expressed as:
y = t * x
To find the value of t, we can use the given information.
From the given information, we know that an item selling for $115.99 has a sales tax of $8.12.
So, we can set up the following equation:
8.12 = t * 115.99
Solving for t:
t = 8.12 / 115.99 ≈ 0.07005
Now we can substitute this value of t into our equation for y:
y = 0.07005 * x
Rounding the coefficient to two decimal places, the mathematical model that gives the amount of sales tax y in terms of the retail price x is:
y = 0.07 * x
To find the sales tax on a $530.50 purchase, we substitute x = 530.50 into the equation:
y = 0.07 * 530.50 ≈ $37.14
Therefore, the sales tax on a $530.50 purchase is approximately $37.14.
To find the mathematical model that gives the amount of sales tax y in terms of the retail price x, we can use the information given in the problem. We know that the sales tax is based on the retail price, so we can set up a proportional relationship between them.
The problem states that an item that sells for $115.99 has a sales tax of $8.12. We can write this as:
115.99 * k = 8.12
Where k is the constant of proportionality. To find the value of k, we can divide both sides of the equation by 115.99:
k = 8.12 / 115.99
k ≈ 0.07006 (rounded to five decimal places)
Now we can use this value of k to write the mathematical model that gives the amount of sales tax y in terms of the retail price x:
y = kx
Substituting the value of k, we have:
y = 0.07006x
To find the sales tax on a $530.50 purchase, we can substitute x = 530.50 into the model:
y = 0.07006(530.50)
y ≈ $37.15 (rounded to the nearest cent)
Therefore, the sales tax on a $530.50 purchase would be approximately $37.15.