Respuesta :
Answer:
Theresa needs 14.3 pounds of Brand A mixed nuts and 13.2 pounds of Brand B mixed nuts.
Step-by-step explanation:
Let A represent the brand A mixed nuts and B represent Brand B mixed nuts.
We have been given that farmer Theresa's Produce Stand sells 27.5 lbs. bags. We can represent this information in an equation as:
[tex]A+B=27.5...(1)[/tex]
We are also told that to make her product she combines Brand A mixed nuts which contain 20% peanuts and Brand B mixed nuts which contain 70% peanuts.
We can represent this information in an expression as:
[tex]0.20A+0.70B[/tex]
Since the stand sells 27.5 lbs. bags of mixed nuts that contain 44% peanuts. We can represent this information in an equation as:
[tex]0.20A+0.70B=0.44(27.5)...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.20(27.5-B)+0.70B=0.44(27.5)[/tex]
[tex]5.50-0.20B+0.70B=12.10[/tex]
[tex]5.50+0.50B=12.10[/tex]
[tex]5.50-5.50+0.50B=12.10-5.50[/tex]
[tex]0.50B=6.6[/tex]
[tex]\frac{0.50B}{0.50}=\frac{6.6}{0.50}[/tex]
[tex]B=13.2[/tex]
Therefore, Theresa needs 13.2 pounds of Brand A mixed nuts.
To find amount of Brand B mixed nuts, we will substitute [tex]B=13.2[/tex] in equation (1) as:
[tex]A+13.2=27.5[/tex]
[tex]A+13.2-13.2=27.5-13.2[/tex]
[tex]A=14.3[/tex]
Therefore, Theresa needs 14.3 pounds of Brand B mixed nuts.
