Question

Lesson 18: Use Systems of Equations to Solve Protstems A bag of popcorn and a juice box contains 518 calories. Two bags of popcorn and 6 juice boxes have a total of 1,456 calories. How many calories are in each Bag of popcorn and juice box? A. 182 calories in each bag of popcorn and each juice box B. 259 calories in each bag of popcorn and each juice box C. 364 calories in each bag of popcorn and 121 calories in each juice box D. 413 calories in each bag of popcorn and 105 calories in each juice box

Answer 1

According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:

`x+y=518`

Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:

`2x+6y=1456`

Use this system of equations and solve the problem, this way:

Solve the first equation for x:

`x=518-y`

Use this expression and replace for x in the second equation:

`\begin{gathered} 2(518-y)+6y=1456 \\ 1036-2y+6y=1456 \\ 4y=1456-1036 \\ y=(420)/(4) \\ y=105 \end{gathered}`

Use this value to find the value of x:

`x=518-105=413`

It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.