Answer:
(a) The system that models the situation: [tex]b+c= 280[/tex] and [tex]0.14b+0.07c= 22.4[/tex]
(b) David needs 40 pounds of bread flour and 240 pounds of cake flour.
Step-by-step explanation:
The amount of flour mixture is 280 lb. that is 8% plain flour.
So, the amount of plain flour in the mixture will be: [tex](280*0.08)lb.= 22.4[/tex] lb.
The number of pounds of bread flour and cake flour needed to make the new mixture are [tex]b[/tex] and [tex]c[/tex] respectively.
So, the first equation will be: [tex]b+c= 280 ...................................(1)[/tex]
The bread flour has 14% plain flour and the cake flour has 7% plain flour.
Thus, the amount of plain flour in bread flour [tex]=0.14b[/tex] lb. and the amount of plain flour in cake flour [tex]= 0.07c[/tex] lb.
So, the second equation will be: [tex]0.14b+0.07c= 22.4 ................................(2)[/tex]
From equation (1), we will get: [tex]b= 280-c[/tex]
Now substituting this [tex]b= 280-c[/tex] into equation (2) in place of [tex]b[/tex]........
[tex]0.14(280-c)+0.07c= 22.4\\ \\ 39.2-0.14c+0.07c=22.4\\ \\ -0.07c=22.4-39.2\\ \\ -0.07c=-16.8\\ \\ c=\frac{-16.8}{-0.07}=240[/tex]
Plugging this [tex]c=240[/tex] into equation (1), we will get.....
[tex]b+240=280\\ \\ b=280-240=40[/tex]
So, David needs 40 pounds of bread flour and 240 pounds of cake flour.
