Question

A local coffee shop offers a membership. Those who aren't a member, pay full price for a large drink at $7 per drink. For members, they pay $3 per large drink, but also pay a membership fee of $8 per month. Write and solve an equation to show how many large drinks a person would have to buy in a month for a member and non-member to pay the same amountA local coffee shop offers a membership. Those who aren't a member, pay full price for a large drink at $7 per drink. For members, they pay $3 per large drink, but also pay a membership fee of $8 per month. Write and solve an equation to show how many large drinks a person would have to buy in a month for a member and non-member to pay the same amount

Answer 1

Let's define \( x \) as the number of large drinks bought in a month.

For a non-member, the total cost for drinks is given by:

\[
\text{Cost}_{\text{non-member}} = 7x
\]

For a member, the total cost includes the monthly membership fee plus the cost of the drinks:

\[
\text{Cost}_{\text{member}} = 8 + 3x
\]

To find out how many drinks \( x \) a person would need to buy for the costs to be equal, we can set the two equations equal to each other:

\[
7x = 8 + 3x
\]

Now, we can solve for \( x \). First, we will isolate \( x \) by subtracting \( 3x \) from both sides:

\[
7x - 3x = 8
\]

This simplifies to:

\[
4x = 8
\]

Next, we divide both sides by 4:

\[
x = 2
\]

Thus, a person would need to buy **2** large drinks in a month for the costs of a member and a non-member to be the same.