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Alchen [17]
3 years ago
15

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 $7.1

8 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.
Mathematics
1 answer:
KiRa [710]3 years ago
6 0
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.
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A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the
Kay [80]

Answer:  The required number of quarters in the collection is 11.

Step-by-step explanation:  Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05,   1 dime = $ 0.10   and    1 quarter = $0.25.

Then, according to the given information, we have

x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)

and

y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Comparing the values of y from equations (iv) and (v), we get

47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.

Thus, the required number of quarters in the collection is 11.

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2 years ago
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