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RecommendationsSkill plansMathLanguage artsScienceSocial studiesEE TX StandardsAlgebra 1> U.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go to your gaWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearbyfast food restaurant. On Monday, she purchased 6 hamburger kid meals and 7 chicken nuggetkid meals, for a total of $39. On Thursday, she spent $42 on 8 hamburger kid meals and 6chicken nugget kid meals. How much does each type of meal cost?Each hamburger meal costs $and each chicken nugget meal costs $Submit

Respuesta :

Let x be the cost of a hamburger kid meal and y the cost of a chicken nugget kid meal

Monday: 6 hamburger kid meals and 7 chicken nugget kid meals for a total of $39:

[tex]6x+7y=39[/tex]

Thursday: $42 on 8 hamburger kid meals and 6 chicken nugget meals:

[tex]8x+6y=42[/tex]

System of equations:

[tex]\begin{gathered} 6x+7y=39 \\ 8x+6y=42 \end{gathered}[/tex]

To solve by elimination:

1- Multiply first equation by 4 and second equation by -3

[tex]\begin{gathered} 4(6x+7y=39) \\ 24x+28y=156 \\ \\ -3(8x+6y=42) \\ -24x-18y=-126 \end{gathered}[/tex]

2- Add both equations you get in step 1:

[tex]10y=30[/tex]

3- Use the equation you get in step 2 to solve y:

[tex]\begin{gathered} 10y=30 \\ \text{Divide both sides of the equation into 10} \\ \frac{10}{10}y=\frac{30}{10} \\ \\ y=3 \end{gathered}[/tex]

4- Use the value of y to solve x:

[tex]\begin{gathered} 6x+7y=39 \\ \\ 6x+7(3)=39 \\ 6x+21=39 \\ \\ \text{Subtract 21 in both sides of the equation:} \\ 6x+21-21=39-21 \\ 6x=18 \\ \\ \text{Divide both sides of the equation into 6:} \\ \frac{6}{6}x=\frac{18}{6} \\ \\ x=3 \end{gathered}[/tex]

Solution:

[tex]\begin{gathered} x=3 \\ y=3 \end{gathered}[/tex]Each hamburger meal costs $3 and each chicken nugget meal costs $3
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