Question

At a local coffee shop, if a customer purchases a monthly coffee club card for $6 they will only pay $1.25 for a cup of coffee. Customers who do not have a coffee club card must pay $2.00 for a cup of coffee. For how many cups of coffee will the cost be the same for customers with and without a coffee club card? What will the cost be?

Multiple choice question.
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A)
For 10 cups of coffee the cost will be $8.00 for both sets of customers.

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B)
For 16 cups of coffee the cost will be $8.00 for both sets of customers.

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C)
For 8 cups of coffee the cost will be $10.00 for both sets of customers.

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D)
For 8 cups of coffee the cost will be $16.00 for both sets of customers.

Answer 1

For 8 cups of coffee, the cost will be the same for customers with and without a coffee club card. The total cost at this point will be $16.00 for both, which makes option D) the correct answer.

Step-by-step explanation:

To figure out for how many cups of coffee the cost will be the same for customers with and without a coffee club card, we can set up an equation to represent each situation:

Without coffee club card: Total Cost = 2.00 * number of cups

With coffee club card: Total Cost = 6.00 + 1.25 * number of cups

We will set these two equations equal to each other to find the number of cups where the cost is the same:

2.00 * number of cups = 6.00 + 1.25 * number of cups

To solve for the number of cups, we subtract 1.25 * number of cups from both sides:

2.00 * number of cups - 1.25 * number of cups = 6.00

0.75 * number of cups = 6.00

Dividing both sides by 0.75 gives us the number of cups:

number of cups = 6.00 / 0.75

number of cups = 8

Now, we calculate the total cost for 8 cups with a coffee club card:

Total Cost = 6.00 + 1.25 * 8

Total Cost = 6.00 + 10.00

Total Cost = 16.00

Therefore, for 8 cups of coffee the cost will be $16.00 for customers with and without a coffee club card. The correct answer is D).