finding percentages

Question

A cattleman wants to mix 2,300 pounds of cattle feed that is to be 14% protein. Barley (11.7% protein) will make up 20% of the mixture. The remaining 80% will be made up of oats (11.8% protein) and soybean meal (44.5% protein). How many pounds of each should he use? (Round your answers to the nearest pound.)

Answer 1

2300 pounds of 14% protein

by mixing Barley 11% protein,- 20% or 1/5 of 2300 = 460 lbs

with Soybean 44.5% protein

and Oats 11.8% protein

O + S = 2300-460 = 1840 lbs

O= 1840-S

B=460

very roughly 140 lbs S, 2160 B and O, B =460 lbs O=1700

O &B each about 12%, S about 44%

44-14 =30

14-12=2

30/2=15 times as much O&B as S

2160= about 15 x 140=2100

.117B +.118O+.117

.117)(.20(2300) + .118(1840-S) + .445S = .14(2300)

.445S-.118S = .14(2300)-.0234(2300)- .118(2300-460)

.327S = (.14-.0234-.118)(2300) + .118(460)

S = (-.0014)(2300)+.118(460))/.327

=(-23(.14)+46(1.18)/.327

=(-2.8-.42+47.2+7.08)/.327

= (49.26-3.22)/.347

= 46.04/.347

=about 132.68 lbs Soy

460 lbs. Barley

Oats = 2300-460-132.68=1840-132.68=1707.32 lbs