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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased 5 hamburger kid meals and 5 chicken nugget kid meals, for a total of $40. On Thursday, she spent $44 on 4 hamburger kid meals and 7 chicken nugget kid meals. How much does each type of meal cost?

Respuesta :

Let h and c be the cost of the hamburger and chicken, respectively. Then, the first statement "5 hamburger and 5 chicken for a total of $40" can be written as

[tex]5h+5c=40[/tex]

and the second statement "4 hamburger and 7 chicken for $44" can be written as

[tex]4h+7c=44[/tex]

Then, we have the following system of equaitons:

[tex]\begin{gathered} 5h+5c=40 \\ 4h+7c=44 \end{gathered}[/tex]

Solving by elimination method.

By multiplying the frist equation by -4 and the second one by 5, we have an equivalent system of equations:

[tex]\begin{gathered} -20h-20c=-160 \\ 20h+35c=220 \end{gathered}[/tex]

So, the variable h has opposite coefficients then by adding both equations we can eliminate variable h, that is,

[tex]15c=60[/tex]

Then, c is given by

[tex]\begin{gathered} c=\frac{60}{15} \\ c=4 \end{gathered}[/tex]

Finally, we can find h by substituting this result into one of the 2 equations of our system. If we choose equation 1, we get

[tex]5h+5(4)=40[/tex]

which gives

[tex]\begin{gathered} 5h+20=40 \\ 5h=20 \\ \text{then,} \\ h=\frac{20}{5} \\ h=4 \end{gathered}[/tex]

Therefore, the cost of the hamburger is $4 and the cost of the chicken is $4 too

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