Respuesta :
EXPLANATION:
We are given the following;
A farmer wants to make a 70% protein ration
The mix would have;
75% protein supplement
25% protein ration
1800 pounds mix of 70% protein ration
From these details we can make out the following;
[tex]\begin{gathered} Supplement=75\%\text{ of x pounds} \\ \text{Ration}=25\%\text{ of (}1800-x)pounds \\ \text{Mixture}=70\%\text{ of }1800\text{ pounds} \end{gathered}[/tex]Take note that the mixture would be made up of protein supplements and protein rations. Hence, the total mix of 1800 pounds would be'
Supplements + Ration = Mixture
Where Supplements is x pounds, then Ration would be 1800 minus x to derive the total weight of Ration.
We can now simplify the equations we came up with and we'll have;
[tex]\begin{gathered} 75x+(25\lbrack1800-x\rbrack)=70\times1800 \\ 75x+(45000-25x)=126000 \\ 75x+45000-25x=126000 \end{gathered}[/tex][tex]\begin{gathered} 75x-25x=126000-45000 \\ 50x=81000 \end{gathered}[/tex]Divide both sides by 50;
[tex]\begin{gathered} \frac{50x}{50}=\frac{81000}{50} \\ x=1620 \end{gathered}[/tex]Therefore, for the protein supplement we would have;
[tex]\begin{gathered} 75\%\text{ of 1620}=0.75\times1620 \\ =1215 \end{gathered}[/tex]Also, for the protein ration;
[tex]\begin{gathered} \text{Mixture}=\text{Supplement}+\text{Ration} \\ 1800=1215+\text{Ration} \\ 1800-1215=\text{Ration} \\ 585=Ration \end{gathered}[/tex]ANSWER:
Protein Supplement = 1215 pounds
Protein Ration = 585 pounds
