Question

soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240lb mixture that is 8% protein?
How many pounds of cornmeal should be in the mixture?

How many pounds of the soybean meal should be in the mixture?

Answer 1

i should make a template for this one. seen it maybe 8 times no lie. what book does it come from?

Answer 2

its off of a final. Im stumped and cannot figure it out.

Answer 3

8% of 240 is .08*240= 19.2 is as start, so you know you want to end up with 19.2 pounds of protein all together

Answer 4

lets say x is the number of pounds of soybean, then
\[.12x\] is the number of pounds of protein in it

Answer 5

and if you have x pounds of soybeans, since the total is 240 you know you have 240 - x pounds of cornmeal.

Answer 6

this is clear i hope. for example if you have 100 soybeans then you have 240 - 100 = 140 pounds of cornmeal

Answer 7

it contributes
\[.06\times (240-x)\] pounds of protein, that is 6% of the number of pounds of cornmeal. so the total pounds of protein is
\[.12x+.06(240-x)\] and you want this to be 19.2 so set
\[.12x+.06(240-x)=19.2\] and solve for x

Answer 8

i have been long winded because i hope if you see a different problem you could translate that as well. now you have to solve the equation. do you need help with that? i will be happy to show you the steps

Answer 9

do you subtract 19.2 to from 240 to get x?

Answer 10

no lets do the steps to solve for x

Answer 11

okay. Thank you.

Answer 12

i don't like decimals much, so i would multiply everything by 100 to remove them. that is, move each decimal over 2 places

Answer 13

\[12x+6(240-x)=1920\] is that step clear?

Answer 14

yes.

Answer 15

now you have to use the distributive law to remove the parentheses
you get
\[12x+1440-6x=1920\]

Answer 16

i multiplied by 6 in the parentheses.
now you have to combine like terms on the right:
\[6x+1440=1920\]

Answer 17

if you don't understand a step, please ask

Answer 18

the last step was
\[12x-6x=6x\]

Answer 19

i understood that part.

Answer 20

ok so now we have
\[6x+1440=1920\] and now you can finally solve for x. subtract 1440 from both sides, then divide by 6. let me know what you get

Answer 21

80?

Answer 22

yes!

Answer 23

awesome

Answer 24

at the beginning i wrote "x = number of pounds of soybeans" so you know that the number of pounds of soybeans is 80 and therefore the number of pounds of cornmeal is 240 - 80 = 160.

80 pounds of soybeans, 160 pounds of cornmeal

Answer 25

one more thing if you are still there.

Answer 26

okay.

Answer 27

when you start out one of these problems, don't just start by writing an equation in x. state what x is. write it down. that way at the end you know what you have solved for. and don't write

"x = soybeans" x is not soybeans, soybeans are soybeans, x is a number. so write
"x = the number of pounds of soybeans" or
"x= the number of gallons of 4% solution" or whatever. it will really help you

Answer 28

i hope all the steps are clear enough that you could try one on your own.

Answer 29

they have been helpful.