Question

13. Jody is supplying his food truck for the week. He buys 32 pounds of pork and 50 pounds of chicken for a total of $185. He realizes he did not purchase enough of either and returns to buy 8 more pounds of pool and 20 more pounds of chicken for a total of $65.60. Which inequality represents the situation above if x represents the cost of pork and y represents the cost of chicken?

Answer 1

Pork is $1.75 per pound (x=1.75)

Chicken is $2.58 per pound (y=2.58)

Explanation:

Key skills needed for this problem: Linear Equations, Systems, Elimination

1) Use x and y for the pork and the chicken and you will get 2 equations:

• 32x + 50y = 185
• 8x + 20y = 65.6

We can use elimination in this system.

2) To use elimination, we can multiply the 2nd equation by -4:

-4(8x + 20y) = 65.6(-4) becomes -32x-80y = -262.40

3) Next add both equations:

32x + 50y = 185

+

-32x - 80y = -262.4

-----------------------------

-30y = -77.4

y = $2.58

4) Next we can substitute the y value into one of the equations. I like the first one so I used that one ---> 32x + 50(2.58) = 185

50(2.58) is equal to 129 so ---> 32x + 129 = 185

-129 -129

------------------------

32x = 56

Divide by 32 and get x= $1.75

5) Therefore, It is $1.75 per pound of pork, and $2.58 per pound of beef.

Hope you understood and have a nice day!! :D