Answer :
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:
[tex]\begin{gathered} 75x+50y=362.5 \\ 30x+40y=200 \end{gathered}[/tex]The solution to the system will be as follows:
[tex]\begin{gathered} 75x+50y=362.5\rightarrow(\times40) \\ 30x+40y=200\rightarrow(\times-50) \\ ----------------- \\ 3000x+2000y=14500 \\ -1500x-2000y=-10000 \\ ----------------- \\ 3000x-1500x=14500-10000 \\ 1500x=4500 \\ x=\frac{4500}{1500}=3 \end{gathered}[/tex]Substitute with x into the first equation to find y
[tex]\begin{gathered} 75\cdot3+50y=362.5 \\ 225+50y=362.5 \\ 50y=362.5-225 \\ 50y=137.5 \\ y=\frac{137.5}{50}=2.75 \end{gathered}[/tex]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