Question

LearningDiagnosticAnalyticsSocial studiesTX StandardsRecommendationsSkill plansScienceA MathLE Language artsYou have prizes to reveal! Go to your gaAlgebra 1> 0.11 Solve a system of equations using elimination: word problems NHRWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanksMrs. Lee sometimes makes her melon salad for special events. When she made it a couplemonths ago, she used 3 kilograms of honeydew melon and 3 kilograms of watermelon, whichcost her $12. Today, she used 2 kilograms of honeydew melon and 1 kilogram of watermelon,spending a total of $6 on the melons. Assuming that the prices of the melons haven'tchanged, how much does a kilogram of each type of melon cost?Honeydew melon costs $|| per kilogram and watermelon costs $ per kilogram.ОСSSubrajt

Answer 1

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:

`3x+3y=12_{\text{ }}(1)`

She also used 2 kilograms of honeydew melon and 1 kilogram of watermelon, spending a total of $6 on the melons. So:

`2x+y=6_{\text{ }}(2)`

From (2) solve for y:

`y=6-2x_{\text{ }}(3)`

Replace (3) into (1):

`\begin{gathered} 3x+3(6-2x)=12 \\ 3x+18-6x=12 \\ -3x=-6 \\ x=-(6)/(-3) \\ x=2 \end{gathered}`

Replace x into (3):

`\begin{gathered} y=6-2(2) \\ y=2 \end{gathered}`

Answer:

Honeydew melon costs 2 dollars per kilogram

Watermelon costs 2 dollars per kilogram