Questions: Beth is buying coffee for everyone in her study group. If she goes to the café next to her school, it will cost her 3.25 per coffee. If she goes to the café by her home, it will cost her 3.75 per coffee, but she has a coupon for 5 off. How many coffees would Beth need to buy for the two options to cost the same?

Beth is buying coffee for everyone in her study group. If she goes to the café next to her school, it will cost her 3.25 per coffee. If she goes to the café by her home, it will cost her 3.75 per coffee, but she has a coupon for 5 off.

How many coffees would Beth need to buy for the two options to cost the same?

Transcript text: Beth is buying coffee for everyone in her study group. If she goes to the café next to her school, it will cost her $3.25 per coffee. If she goes to the café by her home, it will cost her $3.75 per coffee, but she has a coupon for $5 off. How many coffees would Beth need to buy for the two options to cost the same?

Solution

Solution Steps

To find out how many coffees Beth needs to buy for the two options to cost the same, we need to set up an equation where the total cost from both cafés is equal. Let $ x $ be the number of coffees. The cost from the café next to her school is $ 3.25x $. The cost from the café by her home, with the coupon applied, is $ 3.75x - 5 $. We set these two expressions equal to each other and solve for $ x $.

Step 1: Set Up the Equation

Let $ x $ be the number of coffees Beth buys. The cost from the café next to her school is given by $ 3.25x $, and the cost from the café by her home, after applying the coupon, is $ 3.75x - 5 $. We set these two costs equal to each other:

\[ 3.25x = 3.75x - 5 \]

Step 2: Solve the Equation

To solve for $ x $, we first rearrange the equation:

\[ 3.25x - 3.75x = -5 \]

This simplifies to:

\[ -0.5x = -5 \]

Dividing both sides by $-0.5$ gives:

\[ x = 10 \]