Question

4. Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following week and bought 1.2 pounds of gummy bears and 1.5 pounds of jelly beans and paid $15.09. What is the price per pound of each type of candy?Directions: For each problem - define your variables, set up a system of equations, and solve.

Answer 1

Let

the price of gummy bears per pound = x

the price of jelly beans per pound = y

`\begin{gathered} 1.8x+0.6y=10.26 \\ 1.2x+1.5y=15.09 \\ 1.2x=15.09-1.5y \\ x=12.575-1.25y \\ \\ 1.8(12.575-1.25y)+0.6y=10.26 \\ 22.635-2.25y+0.6y=10.26 \\ -1.65y=10.26-22.635 \\ -1.65y=-12.375 \\ y=(-12.375)/(-1.65) \\ y=7.5 \\ \\ 1.8x+0.6y=10.26 \\ 1.8x+0.6(7.5)=10.26 \\ 1.8x+4.5=10.26 \\ 1.8x=10.26-4.5 \\ 1.8x=5.76 \\ x=(5.76)/(1.8) \\ x=3.2 \end{gathered}`

price per pound of gummy bear = $3.2

price per pound of jelly beans = $7.5