Question

One bar of candy A and two bars of candy B have 780 calories. Two bars of candy A and one bar of candy B contain 783 calories. Find the caloric content of each candy bar. Guide Candy bar A contains calories and candy bar B contains calories

Answer 1

Let A be the number of calories that contains candy bar A and let B be the number of calories that contains candy bar B. Then, given the information on the problem, we have the following system of equations:

`\begin{gathered} A+2B=780 \\ 2A+B=783 \end{gathered}`

solving the first equation for A, we get:

`A=780-2B`

substituing this expression on the second equation, we get the following:

`\begin{gathered} 2(780-2B)+B=783 \\ \Rightarrow1560-4B+B=783 \\ \Rightarrow-3B=7833-1560=-777 \\ \Rightarrow B=(-777)/(-3)=259 \\ B=259 \end{gathered}`

now that we have that B = 259, we can find the value of A using the first equation:

`\begin{gathered} A=780-2(259)=780-518=262 \\ \Rightarrow A=262 \end{gathered}`

therefore, candy bar A contains 262 calories and candy bar B contains 259 calories