Question

Jeremiah is making a shake by mixing two different protein powders, measured in ounces. The strawberry-flavored powder has 4 grams of protein per ounce. The banana-flavored powder has 3 grams of protein per ounce. He wants the drink to have a total of 6 ounces of powder and contain 22 grams of protein.

Answer 1

Questions

A. Create a system of linear equations to represent the situation that will determine the exact number of ounces needed for each power.
B. Based on the system you wrote, which algebraic method of solving systems of equations will you choose to solve the system? Explain your choice.
C.Solve the system algebraically, showing your work. Then interpret the solution by explaining what your solution represents in the context of the problem.

Answer 2

Dear Chosen: How about starting by identifying your variables? Represent the weight of the strawberry-flavored powder by one variable (your choice) and that of the banana-flavored powder by another variable (your choice). We're going to use some of each powder. What will the total number of ounces of the powders used be? Can you represent this fact in an equation?

Answer 3

Try it. I'd be glad to continue working with you after I've heard back from you.

Answer 4

ok

Answer 5

so i need two equations

Answer 6

That seems to be a logical conclusion. You have two variables here: one representing the weight of one flavored powder, the other representing the weight of the other flavored powder. To solve a system involving two variables, you need two equations.

What will the total number of ounces of the powders used be? Can you represent this fact in an equation?

Answer 7

Did your shake bring all boys to the yard?

Answer 8

shut up

Answer 9

Chosen: Have you Chosen two variables to represent the weights of the strawberry- and banana-flavored powders yet?

Answer 10

those this two work? @mathmale
4x + 3x = 22
&
4x + 3x = 6

Answer 11

The first equation is great! Nice work! That's the tougher one to write.
Mind explaining what that 6 represents?

Answer 12

6 ounces? i think

Answer 13

Right. In other words, you want a total of 6 oz. of flavored powders.

Answer 14

yea

Answer 15

OK. We know that the strawberry-flavored powder contains 4 grams of protein per oz. We also know that x represents the weight, in oz., of that powder used.
What happens if we multiply (grams of protein per oz.) by (number of oz.)?
As you said, the 6 represents weight only.

Answer 16

Have you Chosen to continue working on this problem or not?

Answer 17

yea im working on it

Answer 18

My point is that there's no place for the 4 and 3 in your second equation. That equation involves weights of powders only, not weights of protein. Does this make sense?

Answer 19

but im kinda confused not sure what to do i think replace x with another number?


and i really dont know know much bout this?

Answer 20

Your 4x + 3x = 22
&
4x + 3x = 6 constitute a great start. Note that the first equation is a measure of grams of PROTEIN only (we want a total of 22 grams of protein, don't we?). The second equation should be (but is not yet) a measure of grams of POWDER (not of protein).
Sorry to have been so roundabout there. My point is that the rates 4 and 3 belong in the first equation but NOT in the second equation.

Answer 21

So, how would you now write that system of linear equations?

Answer 22

LET ME SEE

Answer 23

OK

Answer 24

ooh ok i get what u mean i didnt see any other numbers so i just figured to put those in the 2 equation

Answer 25

Chosen: Your goal here is to come up with two equations in two unknowns. Your first equation is perfect: 4x + 3y = 22. Your second equation becomes perfect if you'll omit the (rates) 4 and 3 from it: x + y + 6.

So, your system of linear equations is x + y = 6 and 4x + 3y = 22. Among the various methods of solving such a system are elimination by substitution (or) addition/subtraction, grahing, determinants, matrices. Which are you going to use to solve this system for x ane y?

Answer 26

umm i guess elimination? help me here bro

Answer 27

OK: Choose one: substitution or addition/subtraction.

Answer 28

add and sub!

Answer 29

OK
You have 4x + 3y = 22
and x + y = 6
Would you mind multiplying every term of the second equation by -4?
Try it (and while you're doing so, ask yourself why we'd do that).

Answer 30

yea i wasjust askin myself that but ok give a sec

Answer 31

-4( x + y = 6) => ?

Answer 32

im guessing it would be -4x + -4y = -24

Answer 33

is that correct?

Answer 34

Yes, that's fine, except that you no longer need the (+) sign. So, you end up with -4x - 4y = -24.
Now align these two equations as follows:

4x + 3y = 22
-4x - 4y = -24

Please add them together. Note how the x terms disappear. Your result?

Answer 35

oh right forgot that ok can u come back like in half an hour CAUSE MY MOTHER ASK ME TO G get some groceries?

Answer 36

I can't promise I'll be back in half an hour, but I will certainly respond to anything you post. Out of curiosity: where are you located? I'm in Tehachapi, Kern County, California.

Answer 37

hah lol ok i hope so and im in Florida Fort Lauderdale!

Answer 38

Wow. Great working with you. Go ahead with your errands. Hope to connect again soon.