Question

Write a systems of equations for problem, define variables used. Please show all work.a butcher buys 75 pounds of ground sirloin and 50 pounds of flank steak for a total cost of $362.50 a second purchase, at the same price, includes 30 pounds of ground sirloin and 40 pounds of flank steak for a total cost of $200 Find the cost of the ground sirloin and the flank steak.

Answer 1

Given:

Let the cost of one pound of ground sirloin = x

And, the cost of one pound of flank steak = y

A butcher buys 75 pounds of ground sirloin and 50 pounds of flank steak for a total cost of $362.50

So, 75x + 50y = 362.5

A second purchase, at the same price, includes 30 pounds of ground sirloin and 40 pounds of flank steak for a total cost of $200

So, 30x + 40y = 200

So, we have the following system of equations:

`\begin{gathered} 75x+50y=362.5 \\ 30x+40y=200 \end{gathered}`

The solution to the system will be as follows:

`\begin{gathered} 75x+50y=362.5\rightarrow(*40) \\ 30x+40y=200\rightarrow(*-50) \\ ----------------- \\ 3000x+2000y=14500 \\ -1500x-2000y=-10000 \\ ----------------- \\ 3000x-1500x=14500-10000 \\ 1500x=4500 \\ x=(4500)/(1500)=3 \end{gathered}`

Substitute with x into the first equation to find y

`\begin{gathered} 75\cdot3+50y=362.5 \\ 225+50y=362.5 \\ 50y=362.5-225 \\ 50y=137.5 \\ y=(137.5)/(50)=2.75 \end{gathered}`

So, the answer will be:

The cost of one pound of ground sirloin = x = $3

The cost of one pound of flank steak = $2.75