Let:
x = Cost of each kilogram of honey drew
y = Cost of each kilogram of watermelon
Once, she used 3 kilograms of honeydew melon and 3 kilograms of watermelon, which cost her $12. So:
[tex]3x+3y=12_{\text{ }}(1)[/tex]She also used 2 kilograms of honeydew melon and 1 kilogram of watermelon, spending a total of $6 on the melons. So:
[tex]2x+y=6_{\text{ }}(2)[/tex]From (2) solve for y:
[tex]y=6-2x_{\text{ }}(3)[/tex]Replace (3) into (1):
[tex]\begin{gathered} 3x+3(6-2x)=12 \\ 3x+18-6x=12 \\ -3x=-6 \\ x=-\frac{6}{-3} \\ x=2 \end{gathered}[/tex]Replace x into (3):
[tex]\begin{gathered} y=6-2(2) \\ y=2 \end{gathered}[/tex]Answer:
Honeydew melon costs 2 dollars per kilogram
Watermelon costs 2 dollars per kilogram
