Question

Mr. Torres spent $30.00 to buy 9 1··2pounds of ground beef and chicken for a family cookout. If the price of ground beef was $3.50 per pound and chicken was $3.00 per pound, how many pounds of each did he buy

Answer 1

Let \( x \) be the number of pounds of ground beef, and \( y \) be the number of pounds of chicken. We have the following system of equations based on the information provided:

1. The total weight of the meat is:
\[
x + y = 9.5
\]

2. The total cost of the meat is:
\[
3.50x + 3.00y = 30.00
\]

Now we can solve these equations step by step.

**Step 1: Solve the first equation for \( y \):**
\[
y = 9.5 - x
\]

**Step 2: Substitute \( y \) into the second equation:**
\[
3.50x + 3.00(9.5 - x) = 30.00
\]

**Step 3: Distribute the 3.00:**
\[
3.50x + 28.50 - 3.00x = 30.00
\]

**Step 4: Combine like terms:**
\[
0.50x + 28.50 = 30.00
\]

**Step 5: Isolate the variable \( x \):**
\[
0.50x = 30.00 - 28.50
\]
\[
0.50x = 1.50
\]

**Step 6: Solve for \( x \):**
\[
x = \frac{1.50}{0.50} = 3
\]

So, he bought 3 pounds of ground beef.

**Step 7: Find \( y \):**
Using the equation \( y = 9.5 - x \):
\[
y = 9.5 - 3 = 6.5
\]

So, he bought 6.5 pounds of chicken.

**Final Result:**
- Ground beef: 3 pounds
- Chicken: 6.5 pounds