Problem

40 The equation $y=6.75 x$ models the cost, in dollars, to purchase $x$ pounds of steak at grocery store 1 . This table shows the cost to buy different weights of steak at grocery store 2 .
Cost of Steak at Grocery Store 2
\begin{tabular}{|c|c|}
\hline Weight (pounds) & Cost \\
\hline 2 & $\$ 15.00$ \\
\hline 3 & $\$ 22.50$ \\
\hline 5 & $\$ 37.50$ \\
\hline 9 & $\$ 67.50$ \\
\hline
\end{tabular}

Answer

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Answer

So, the weight of steak that has the same cost in both grocery stores is approximately \(\boxed{0.90}\) pounds.

Steps

Step 1 :First, we need to find the cost per pound of steak at grocery store 2. We can use the given data in the table to find the cost per pound for each weight.

Step 2 :For 2 pounds: \(\frac{15}{2} = 7.50\) dollars per pound

Step 3 :For 3 pounds: \(\frac{22.50}{3} = 7.50\) dollars per pound

Step 4 :For 5 pounds: \(\frac{37.50}{5} = 7.50\) dollars per pound

Step 5 :For 9 pounds: \(\frac{67.50}{9} = 7.50\) dollars per pound

Step 6 :Now we know that the cost per pound of steak at grocery store 2 is \(7.50\) dollars.

Step 7 :Next, we need to find the weight of steak that has the same cost in both grocery stores.

Step 8 :Let's set the cost of steak at grocery store 1 equal to the cost of steak at grocery store 2: \(6.75x = 7.50x\)

Step 9 :Now, we can solve for x: \(\frac{6.75}{7.50} = x\)

Step 10 :Calculating x, we get: \(x \approx 0.90\)

Step 11 :So, the weight of steak that has the same cost in both grocery stores is approximately \(\boxed{0.90}\) pounds.

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