Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.At a candy store, Carla bought 6 pounds of jelly beans and 6 pounds of gummy worms for $108. Meanwhile, Rachel bought 6 pounds of jelly beans and 1 pound of gummy worms for $63. How much does the candy cost?

Answer 1

Given:

Let x and y be the cost of 1 pound of Jelly beans and 1 pound of gummy worms.

`\begin{gathered} 6x+6y=108 \\ x+y=18\ldots\text{ (1)} \end{gathered}`
`6x+y=63\ldots\text{ (2)}`

Subtract equation (1) from equation(2)

`\begin{gathered} 6x+y-x-y=63-18 \\ 5x=45 \\ x=9 \end{gathered}`

Substitute x=9 in equation(1)

`\begin{gathered} 9+y=18 \\ y=18-9 \\ y=9 \end{gathered}`

Cost of 1 pound of Jelly beans is $9

Cost of 1 pound of gummy worms is $9