Answer: He bought 7 pounds of chicken and 5 pounds of beef
Step-by-step explanation: We shall start by assigning letters to the unknown variables. Hence, let b represent a pound of beef and let c represent a pound of chicken. If Bennett bought a total of 12 pounds of meat, then we can express this as
b + c = 12
Then if he spent a total of $63.7 on both types of meat, we can write it out as
6.3b + 4.6c = 63.7
We now have a pair of simultaneous equations, which are
b + c = 12 --------(1)
6.3b + 4.6c = 63.7 --------(2)
In equation (1) we shall make b the subject of the equation
b = 12 - c
We now substitute for the value of b into equation (2)
6.3(12 - c) + 4.6c = 63.7
75.6 - 6.3c + 4.6c = 63.7
We collect like terms and we now have
-1.7c = -11.9
Divide both sides of the equation by -1.7
c = 7.
Having found the value of c, we can now substitute for the value of c into equation (1)
b + c = 12
b + 7 = 12
Subtract 7 from both sides of the equation
b = 5.
Therefore, Bennett purchased 7 pounds of chicken and 5 pounds of beef.
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