Question

I asked this question yesterday a couple of times in fact but I didn't quite get the solution clearly. I'm game for all the help I can get. Soybean meal is 16% protien and corn meal is 8% protien. How many pounds of each should be mixed together in order to get 320 pounds of mixture that is 12% protien.

Answer 1

x + y = 320
.16x + .08y = .12(320)

Answer 2

Multiply the 2nd equation by 100 (it gets rid of decimal places)

Answer 3

x + y = 320
16x + 8y = 3840

Answer 4

a certain sense of deja vu.
solve
\[.16x=.08(320-x)=.12\times 320\]

Answer 5

Multiply the first equation by -8 so that you can eliminate the y's

Answer 6

\[.16x+.08(320-x)=.12\times 320\] is more like it. or use two variable method as blexting is writing. whatever you find easier

Answer 7

-8(x + y = 320) so....


-8x - 8y = -2560
16x + 8y = 3840

Answer 8

8x = 1280
x = 160

so if x + y = 320, then y = 160

Answer 9

@satellite - I prefer teaching with the two variable method as it keeps things simple for the learner. They have a hard time turning words into equations as is. Going to your method requires skipping a lot of intermediate steps and can be hard to grasp for most learners.

Answer 10

blexting, that's what I got , 160-it's an equal amount of both. I just wanted to be sure.Thank you very much.

Answer 11

I think both methods are fine

Answer 12

i agree with GT......

Answer 13

if that is your preference. i prefer one variable because it is easier to explain how to solve a linear equation than a solution.
in this particular example i would use no equation since 12 is half way between 8 and 16

Answer 14

I used GT's method and finnaly got it.Thanks everybody.

Answer 15

*system

Answer 16

Mission accomplished! That is the goal. Specific method is almost besides the point.

Answer 17

satellite actually GT was right it is easy for those who play with numbers but for those who really dont love them it will be like a horror show

Answer 18

usually satellite's method is the first one taught...substitution..

x+y=320
so y=320-x....substitute and solve...I really don't see anything complicated here

Answer 19

soy soy protein corn corn protein total goal
100 16 220 17.6 33.6 38.4 nope
200 32 120 9.6 41.6 nope

i find this approach will actually give a better understand of exactly what is going on and how to set up the equation

Answer 20

Linear Programming ???????????
Hahahaha it will be more difficult to understand

Answer 21

soy soy protein corn corn protein total goal
100 16 220 17.6 33.6 38.4 nope
200 32 120 9.6 41.6 nope

x .16x 320 - x .08(320-x) .16x + .08(320-x) = 38.4

Answer 22

this is not linear programming at all. i say "lets try it if we use 100 pounds soy" and see what we get."

Answer 23

then u can even use LInear Programming it will be easier to calculate..........

Answer 24

@satellite - at the end of the day, it is a problem of two unknowns with two pieces of information that result in two equations. Substitution method is nothing but a "skip" a couple of steps way of solving the two equations. Either works. But, using one will keep things consistent and focused for many learners on this forum who seem to have a hard time grasping math word problems.

Answer 25

@gt i respect your opinions but respectfully disagree.
i just went through this very topic two weeks ago, and in fact used both methods. (trying to make the point that there is not one way to solve a problem but in fact many). it wasn't this boring problem, but a rather simpler one at first, with nice whole numbers, like "the sum of the ages is 36 and the difference is 12 what are the ages"
solved it 6 ways in total,
the two variable approach was the least popular.
as for the mixture problems, ( i use wine and gin or plain and peanut m&ms,) the problem is not what approach to use, but how to set up and equation. if you use specific examples with specific numbers the equation will become clear to everyone.

solving the system i have found to be much much harder (yes, zarkon, i know it is not hard to do, i am talking about students whose level of algebra fairly low)