# Thread: Applications of Systems,

1. ## Applications of Systems,

Problem 1
-Soybean meal is 16% protein; corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 pound mixture that is 12% protein?

And someone please check if I did this problem correctly....
The difference between two numbers is 11. Twice the smaller number plus three times the larger is 123. What are the numbers?
I got 90 and 101 is that correct?

2. Originally Posted by dvnswl
Problem 1
-Soybean meal is 16% protein; corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 pound mixture that is 12% protein?
Let $\displaystyle x$ be the mass of soybean in the mix and $\displaystyle y$
be the mass of corn meal in the mix.

Then as these add to $\displaystyle 350$ pounds:

$\displaystyle x+y=350$.

The mass of protien in the mix is:

$\displaystyle \mbox{mass of protien}=0.16x+0.09y$,

which is 12% of the total mass, so:

$\displaystyle \frac{0.16x+0.09y}{350}=0.12$,

which may be rearranged to:

$\displaystyle 16x+9y=4200$.

So now you have a pair of simultaneous linear
equations in x and y to solve.

RonL

3. Originally Posted by dvnswl

And someone please check if I did this problem correctly....
The difference between two numbers is 11. Twice the smaller number plus three times the larger is 123. What are the numbers?
I got 90 and 101 is that correct?
Since twice 90 is greater than 123, your answer cannot be right.

Let the numbers be $\displaystyle x$ and $\displaystyle y$ with $\displaystyle x>y$, then:

$\displaystyle x-y=11$,

and:

$\displaystyle 3x+2y=123$

Now twice the first equation plus the second gives:

$\displaystyle 2(x-y) + (3x+2y) = 22+123$,

or:

$\displaystyle 5x=145$,

so:

$\displaystyle x=145/5 = 29$,

and then:

$\displaystyle y= 18$.

RonL