beth is buying coffee for everyone in her study group. if she goes to the café next to her school, it will…
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? coffees
Answer
Explanation:
Step1: Set up cost - equations
Let $x$ be the number of coffees. The cost $C_1$ of the school - cafe is $C_1 = 3.25x$. The cost $C_2$ of the home - cafe is $C_2=3.75x - 5$.
Step2: Set the two costs equal
We want to find when $C_1 = C_2$, so we set up the equation $3.25x=3.75x - 5$.
Step3: Solve the equation for $x$
First, subtract $3.25x$ from both sides: $0 = 3.75x-3.25x - 5$. Then simplify the right - hand side: $0 = 0.5x - 5$. Add 5 to both sides: $5 = 0.5x$. Divide both sides by $0.5$: $x=\frac{5}{0.5}=10$.
Answer:
10