Question

Can someone tell me where I went wrong? Livestock feed. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed to get a 350-lb mixture that is 12% protein? Here is what I came up with.
Let s = pounds of soybean

Let c = pounds of corn meal

s + c = 350

16s = 9c = 12 ( s+c) = 12(350)2

-9s-9c +165 + 9c

= 3150 + 4200

7s =1050àdivide by 7

S= 150

150+ c = 350

150 + 200

150 + 200=350

C= 200

Answer 1

My teacher said this was wrong 16s = 9c = 12 ( s+c) = 12(350)2 ; incorrect
and then gave me this hint, but i am confused Let s be the Soybean meal, and let c be the corn meal
Write an equation so that the sum of s and c is 350 lbs
Then write a second equation that the sum of 16% s and 9% c is 12% of 350.
Then solve for s and c.

Answer 2

@andjie your first equation s + c = 350 is correct! For your second equation, percents should be expressed as decimals. It should be 0.16s + 0.09c = 0.12(350). Do you understand?

Answer 3

you can multiply everything in equation 2 by 100 to get 16s+9c = 12*350

Answer 4

easier to go right to
\[16x+9(350-x)=12\times 350\]

Answer 5

if you put \(x\) as the amount of soy, the amount of corn must be \(350-x\)

Answer 6

@calculusfunctions How was mine wrong if you can explain that and was that the only thing wrong with my whole solution

Answer 7

See that is the probelm after that happens I get confused on my whole set up

Answer 8

@andjie the second equation is in terms of the amount of protein in the mixture. A percent is a measurement out of 100. Thus 36% for example, would be 36/100 or 0.36. Now if there are s pounds of soybean and soybean has 16% pounds of protein, then the part that is 16% is 0.16s. Similarly for cornmeal it is 0.09c. Now there is 12% protein in the mixture of the two, and there is 350 lb of the mixture., hence the total amount of protein is
0.12(350). Thus the the second equation should be 0.16s + 0.09c = 0.12(350). Understand?

Answer 9

Wow I understand it now

Answer 10

Thank you so much for helping me understand I was going crazy

Answer 11

Great! Do you want me to stick around to check your solution and final answer?

Answer 12

I would appreciate that I have problems setting everything up

Answer 13

let me see if I can do this

Answer 14

No problem. I'll stay for as long as you need me to.

Answer 15

Nope I still don't have it hold on

Answer 16

That's OK! Don't rush, take your time.

Answer 17

0.16s + 0.9c = 0.12(350)
-0.9s-0.9c +165 + 9c
= 3150 + 4200
7s =1050divide by 7
S= 150
150+ c = 350
150 + 200
150 + 200=350
C= 200

Answer 18

It is like I keep losing what I am suppose to do next it is irritating

Answer 19

No @andjie it's 0.09c, not 0.9c.

Answer 20

s + c = 350
0.16s + 0.09c = 0.12(350)
-0.09s-0.09c +165 + 0.09c
= 3150 + 4200
7s =1050divide by 7
S= 150
150+ c = 350
150 + 200
150 + 200=350
C= 200

Answer 21

YES! c = 200 and s = 150. Perfect!

Answer 22

So that is what I was missing that one tiny aspect although in math terms simple is a big mistake

Answer 23

Yes, do you understand how to deal with percents now?

Answer 24

yes multiply the number by 100 and you will get the decimal form?

Answer 25

You mean divide by 100 to change percents to decimals.

Answer 26

oh divide wow
I will get it

Answer 27

That's OK, you did just fine!

Answer 28

Anything else?

Answer 29

So my setup is complete now

Answer 30

I do have one more question actually I just want you to let me know if I did it correctly if you have time

Answer 31

Sure. Go ahead.

Answer 32

a = 1 + b,
b = 5 − 2a
b = 5-2(1=b)
b = 5-2-2b
b + 2b = 5-2
3b = 3
b = 1
a = 1 + b
a = 1 + 1
a = 2
b = 5 – 2a
1 = 5 – 2(2)
1 = 5 – 4
a=2, b=1
The lines intersect at (2, 1), so they are consistent and are dependant.
a= (0, -1), (3, 2)
b= (0, 5), (3, -1)

Answer 33

Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set−builder notation to write the solution set. If a system has no solution, state this.

Answer 34

@andjie Perfect!!!!

Answer 35

Really!

Answer 36

:)

Answer 37

Yes, really!!!

Answer 38

Awesome thank you for all your help it means the world to me!

Answer 39

Welcome anytime! Anything else right now?

Answer 40

No not right now!