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Jody is supplying his food truck for a week. He buys 32 pounds of pork and 50 pound of chicken for a total of $185. He realizes he did not purchase enough of either and returns to buy 8 more pounds of pork and 20 more pounds of chicken for a total of $65.60. Determine the unit price, in dollars per pound, for the pork and the chicken.

Respuesta :

Pork costs $1.75 per pound and chicken costs $2.58 per pound

Step-by-step explanation:

   Let us assume the cost of unit pound of pork to be [tex]p[/tex] and cost of unit pound of chicken to be [tex]c[/tex]. We are given two instances both of which yield a linear equation in [tex]p[/tex] and[tex]c[/tex].

   The two purchases of meat can be modeled as follows:

[tex]32p+50c=185,8p+20c=65.60[/tex]

Multiplying second equation by 4 and subtracting from 1st equation.

[tex]32p+50c-32p-80c=185-262.40[/tex]

[tex]30c=77.40[/tex]

[tex]c=2.58[/tex]$

[tex]p=1.75[/tex]$

∴ Pork costs $1.75 per pound and chicken costs $2.58 per pound.

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