Question

A fast food restaurant sold 35 burgerswith cheese. If the ratio of burgers soldwith cheese compared to withoutcheese was 7:3, how many burgers didthey sell total?

Answer 1

The total number of burgers sold is: 50

Problem Statement

The question tells us a restaurant sold 35 burgers with cheese and also that the ratio of burgers sold with cheese compared to burgers sold without cheese is 7:3.

We are asked to find the total amount of burgers sold; with and without the cheese.

SOLUTION

The question already told us that the ratio of burgers sold with cheese to those without cheese is 7:3. This means that for every 7 burgers with cheese sold, the restaurant also sold 3 burgers without any cheese.

This further implies that out of 10 burgers sold at a time, the restaurant must have sold 7 cheeseburgers and 3 burgers without cheese.

This means that we can say:

`35\text{ burgers represent }(7)/(10)\text{ of burgers sold by the restaurant}`

If this is the case, then we can also say that:

`(3)/(10)\text{ of the total burgers sold is without cheese}`

Thus, we can write an equation stating that "35 burgers plus 3/10 of the total burgers (B) must be equal to the total number of burgers (B)"

This is done below:

`\begin{gathered} 35+(3)/(10)* B=B \\ 35+(3B)/(10)=B \\ \text{Multiply both sides by 10} \\ 350+3B=10B \\ \text{Subctract 3B from both sides} \\ 350+3B-3B=10B-3B \\ 350=7B \\ \text{Divide both sides by 7} \\ (350)/(7)=(7B)/(7) \\ 50=B \\ \\ \therefore B=50 \end{gathered}`

Final Answer

Thus, the total number of burgers sold is: 50