Question

Please, I NEED HELP. Anyone?

Answer 1

Answer:  

(a) The system that models the situation:   $b+c= 280$ and $0.14b+0.07c= 22.4$

(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:  $(280*0.08)lb.= 22.4$ lb.

The number of pounds of bread flour and cake flour needed to make the new mixture are $b$ and $c$ respectively.

So, the first equation will be:   $b+c= 280 ...................................(1)$

The bread flour has 14% plain flour and the cake flour has 7% plain flour.

Thus, the amount of plain flour in bread flour $=0.14b$ lb. and the amount of plain flour in cake flour $= 0.07c$ lb.

So, the second equation will be:   $0.14b+0.07c= 22.4 ................................(2)$

From equation (1), we will get:   $b= 280-c$

Now substituting this $b= 280-c$ into equation (2) in place of $b$........

$0.14(280-c)+0.07c= 22.4\\ \\ 39.2-0.14c+0.07c=22.4\\ \\ -0.07c=22.4-39.2\\ \\ -0.07c=-16.8\\ \\ c=\frac{-16.8}{-0.07}=240$

Plugging this $c=240$ into equation (1), we will get.....

$b+240=280\\ \\ b=280-240=40$

So, David needs 40 pounds of bread flour and 240 pounds of cake flour.