EXPLANATION:
Given;
We are told that Henry makes a mix of type A and type B coffee. Also he made a total of 124 pounds and that cost a total of $622.95, meanwhile one pound of type A costs $4.05 and one pound of type B costs $5.80.
Required;
We are required to calculate how many pounds of type B was used in the mixture.
Step-by-step solution;
To solve this problem we shall begin by assigning variables to the unknown quantities. We shall call type A coffee x, and type B coffee shall be y.
If Henry made a total of 124 pounds of the coffee blend, then we will have the following equation;
[tex]x+y=124-----(1)[/tex]
Also type A costs $4.05 and type B costs $5.80. If the mixture of both costs $622.95, then we can represent this by the following equation;
[tex]4.05x+5.80y=622.95-----(2)[/tex]
We can now solve the system of equations for x (type A) and y (type B).
We shall start with equation (1), make x the subject of the equation;
[tex]x=124-y[/tex]
Next we substitute the value of x into equation (2);
[tex]\begin{gathered} 4.05x+5.80y=622.95 \\ \\ 4.05(124-y)+5.80y=622.95 \\ 502.2-4.05y+5.80y=622.95 \end{gathered}[/tex][tex]\begin{gathered} 5.80y-4.05y=622.95-502.2 \\ \\ 1.75y=120.75 \end{gathered}[/tex]
We now divide both sides by 1.75;
[tex]\begin{gathered} \frac{1.75y}{1.75}=\frac{120.75}{1.75} \\ \\ y=69 \end{gathered}[/tex]
We can now substitute the value of y back into equation (1);
[tex]\begin{gathered} x+y=124 \\ x+69=124 \\ x=124-69 \\ x=55 \end{gathered}[/tex]
Therefore, Henry used 55 pounds of type A coffee and 69 pounds of type B coffee.
ANSWER:
Type B coffee was 6
