Question

Please, I NEED HELP. Anyone?

1. David would like to make a 280 lb. flour mixture that is 8% plain flour. He has bread flour that is 14% plain and cake flour that is 7% plain Let b represent the number of pounds of bread flour needed to make the new mixture and let c represent the number of pounds cake flour needed


(a) What is the system that models this situation?

(b) How many pounds of bread flour and cake flour will David need? Show your work and label your answers correctly


Hint: Remember to change the percentages into decimals.


Answer:

I would really appreiate the help.

Answer 1

(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.

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=(-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.