Question

CAN SOMEONE PLEASE TELl ME WHAT TWO EQUATIONS I CAN MAKE WITH THIS PROBLEM PLEASEE ITS DUE TOMORROW!!!

PLEASEE HELP ME THIS IS REALLY IMPORTANT ITS DUE TOMORROW AND I DON’T UNDERSTAND IT!!!



At Lyon Café, a cup of coffee costs $2.25. Lyon Café offers a Mug Club discount program. You can join by purchasing a mug for $8.00 and then every time you bring your mug in you get a dollar off your cup of coffee. Sarah plans on purchasing 6 cups of coffee. Should she join the Mug Club? Why or why not? When does the Mug Club cost the same as purchasing coffee without the mug club? What is the total cost? How many cups of coffee would you-need to purchase in order to make the mug club the better deal?

Answer 1

• Sarah should not join Mug Club
• Cost is the same at $18 for 8 cups
• Mug Club is cheaper for more than 8 cups

Explanation:

You want to know when it is cost-effective to join the "Mug Club" for a cost of $8 and savings of $1 per cup of coffee that has a normal cost of $2.25 per cup. Sarah will be buying 6 cups of coffee.

Club cost

It is useful to think about how much money you have to take out of your wallet to pay the costs. For Mug Club, you pay $8 before you get any coffee, and you pay $1.25 for each cup. For x cups of coffee, you pay y dollars:

y = 8 +1.25x

Without Mug Club

When you're not in the Mug Club, your cost is $2.25 per cup:

y = 2.25x

Cost of 6 cups

With Mug Club, the cost of 6 cups of coffee is ...

y = 8 +1.25(6) = 15.50

Without Mug Club, the cost of 6 cups of coffee is ...

y = 2.25(6) = 13.50

Sarah should not join the Mug Club.

Equal costs

The two costs are equal when ...

y = y

8 +1.25x = 2.25x

8 = x . . . . . . . . . . . . . subtract 1.25x from both sides

y = 2.25(8) = 18

The costs are equal at $18 if you buy 8 cups of coffee.

Mug Club is the better deal if you buy more than 8 cups.

Answer 2

• Sarah should not join the Mug Club as it will cost her more when buying 6 cups of coffee than if she wasn't a member of the Mug Club.
• The Mug Club costs the same as purchasing coffee without the Mug Club membership when 8 cups of coffee are purchased.
• The total cost is $18.00.
• You would need to purchase more than 8 cups of coffee in order to make the Mug Club the better deal.

Explanation:

Define the variables:

• Let x be the number of cups of coffee Sarah purchases.
• Let y be the total cost (in dollars).

If a cup of coffee costs $2.25, the equation to represent the total cost of purchasing x cups of coffee would be:

`\boxed{y = 2.25x}`

If Sarah joins the Mug Club, she has to pay $8.00 for a mug but then gets a dollar off each cup of coffee. Therefore, each cup of coffee would cost $1.25.

Therefore, an equation for the total cost of purchasing x cups of coffee when a member of the Mug Club would be:

`\boxed{y = 8 + 1.25x}`

To find the cost of purchasing 6 cups of coffee, input x = 6 into the two equations:

`\begin{aligned}\textsf{Regular customer}\implies y&=2.25(6)\\&=13.50\end{aligned}`

`\begin{aligned}\textsf{Mug Club member} \implies y&=8+1.25(6)\\&=8+7.50\\&=15.50\end{aligned}`

As $15.50 is greater than $13.50, Sarah should not join the Mug Club as it will cost her more when buying 6 cups of coffee than if she wasn't a member of the Mug Club.

To find when the Mug Club costs the same as purchasing coffee without the Mug Club, substitute the first equation into the second equation and solve for x:

`\implies 2.25x=8+1.25x`

`\implies 2.25x-1.25x=8+1.25x-1.25x`

`\implies x=8`

Therefore, the Mug Club costs the same as purchasing coffee without the Mug Club membership when 8 cups of coffee are purchased.

To find the total cost, substitute x = 8 into one of the equations:

`\implies y=2.25(8)=18`

Therefore, the total cost is $18.00.

To calculate how many cups of coffee you would need to purchase in order to make the Mug Club the better deal, set the equation for the Mug Club less than the equation without the Mug Club and solve for x:

`\implies 8+1.25x < 2.25x`

`\implies 8+1.25x-1.25x < 2.25x-1.25x`

`\implies 8 < x`

`\implies x > 8`

Therefore, you would need to purchase more than 8 cups of coffee in order to make the Mug Club the better deal.