Answer:
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