Question

Which shows a correct order to solve this story problem? Kent and Curtis went to the state fair. They had to pay a total of $7.18 sales tax on everything they bought. They spent $22.50 for each admission ticket and $35.50 altogether for food. They split all the costs evenly. How much did each boy pay? A. Step 1: Calculate the price of 2 admission tickets. Step 2: Add that amount to the amount spent on food and the tax. Step 3: Divide by 2. B. Step 1: Double the amount for 1 admission ticket. Step 2: Take half of the amount spent on food and add the total from Step 1 plus the tax. Step 3: Divide by 2. C. Step 1: Add $22.50 and $35.50. Step 2: Divide the total by 2. Step 3: Add the amount of the tax.

Answer 1

The problem is asking how much each person will need to pay. Simplifying the problem into an equation with variables (an algorithm) will greatly help you solve it:

S = Sales Tax = $ 7.18 per any purchase
A = Admission Ticket = $ 22.50 entry price for one person (no tax applied)
F = Food = $ 35.50 purchases for two people

We know the cost for one person was: (22.50) + [(35.50/2) + 7.18] =
$ 47.43 per person. Now we can check each method and see which one is the correct algorithm:

Method A)
[2A + (F + 2S)] / 2 = [ (2)(22.50) + [35.50 + (2)(7.18)] ]/ 2 = $47.43
Method A is the correct answer

Method B)
[(2A + (1/2)F + 2S) /2 = [(2)(22.50) + 35.50(1/2) + (2)7.18] / 2 = $38.55
Wrong answer. This method is incorrect because the tax for both tickets bought are not being used in the equation.

Method C)
[(A + F) / 2 ]+ S = [(22.50 + 35.50) / 2 ] + 7.18 = $35.93
Wrong answer. Incorrect Method. The food cost is being reduced to the cost of one person but admission price is set for two people.