How do I make an equation for this?

Question

Jackson is buying new shoes and a new hat. The shoes cost $40. He spends $59.40 for the shoes and hat after an additional 8% sales tax. How much did the hat cost before tax?

Answer 1

Let h be the cost of the hat before tax.

So the total value of the hat and shoes before tax is h+40.

To express the addition 8% of sales tax, taken on top of the hat and shoes, it would be 1.08 * (h+40). Note - 8% converted to a decimal is 0.08.

You are given the value 59.40 for this after tax amount.

So the final equation would be 1.08(h+40)= 59.40.

Answer 2

For purposes of solving this problem, we’ll assume that both the hat and the shoes are taxable items. The shoes cost $40 before tax and the hat costs $h before tax. The tax rate is 8%, meaning we need to multiply the pre-tax price by 1.08 to calculate the price after tax.

So 1.08(40+h) = 59.40

43.20 + 1.08h = 59.40

43.20 - 43.20 + 1.08h = 59.40 - 43.20

1.08h = 16.20

h= 16.20/1.08

h= 15 so the price of the hat before tax was $15.00.

Answer 3

Let X be the cost of the hat before tax.

The shoes cost $40. The total amount Jackson spends for both the shoes and the hat after an 8% sales tax is $59.40.

The total cost before tax for the shoes and the hat is:

Total cost before tax = Cost of shoes + Cost of hat = 40 + X

The total cost after adding 8% sales tax is given by:

Total cost after tax = Total cost before tax * (1+Sales tax rate) = (40 + X) * 1.08

According to the problem, the total cost after tax is 59.40, so the equation will be:

(40 + X) * 1.08 = 59.40

Now, solve for X. You should get X value as $15.