Question

Mr. Torres spent $40.00 to buy 18 pounds of ground beef and chicken for a family to cook out. If the price of ground beef was $4.00 per pound and the chicken was $2.00 per pound, how many pounds of each did he buy?

Answer 1

2 pounds of ground beef
16 pounds of chicken

Answer 2

They bought 2 pounds of ground beef and 16 pounds of ground chicken.

Explanation:

Let b be the beef, and c be the chicken:

b + c = 18, the pounds of beef and the pounds of chicken added equal 18 pounds

4b + 2c = 40, the beef costs 4 dollars per pound and the chicken costs 2 dollars per pound. They add up to 40 dollars total.

Use the equation b + c = 18 and subtract c from both sides to get b = 18 - c. We replace this equation with b in 4b + 2c = 40 to get 4(18 - c) + 2c = 40 because b is 18 - c.

Now we solve for c:

4(18 - c) + 2c = 40

Simplify:

72 - 4c + 2c = 40

Combine Like Terms:

72 - 2c = 40

subtract 72 from both sides:

-2c = -32

Divide Both Sides by 2:

-c = -16

Make the Equation Positive:

c = 16

Okay cool, now we know that they bought 16 pounds of chicken, to find out how much beef the bought, replace c by 16 in b + c = 18 to get b + 16 = 18

b + 16 = 18

Subtract 16 from both sides:

b = 2, they bought 2 pounds of beef

To check, replace c with 16 and b with 2 in 4b + 2c = 40 to get

4(2) + 2(16) = 40

Multiply:

8 + 32 = 40

40 = 40

The equation is true