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

a. Create a system of linear equations to represent the situation that will determine the exact number of ounces needed for each power.

Answer 2

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.

Answer 3

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 4

@Ashleyisakitty

Answer 5

First choose variables to represent ounces of each powder. e.g. S=ounces of strawberry; B=ounces of banana.

You'll need two equations for two unknowns. One equation will represent the total number of ounces of powder, the other equation will represent the grams of protein.

Answer 6

4x + 3x = 22?

Answer 7

@CliffSedge

Answer 8

Yes, that would be an equation representing grams of protein with x=strawberry and y=banana.

Answer 9

So you need another equation to represent the total number of ounces of both powders.

Answer 10

x + y = 6?

Answer 11

That'll do it. There are now many different methods you could use to solve the system. I'd go with substitution, personally.

Answer 12

ok

Answer 13

is that it for part A?

Answer 14

Yep, part A is just to write the system (the two equations).

Answer 15

And Part B is substitution?

Answer 16

@CliffSedge

Answer 17

Part B is whatever you want, but you have to give a reason why you pick whatever method. I personally like substitution in this situation, but you might like something else.

Answer 18

Maybe you'd rather solve by graphing or using Cramer's rule or Gauss-Jordan elimination (though that is a bit overkill on a 2by3 system . . .)

Answer 19

could you explain how you would solve it with substitution?

Answer 20

@CliffSedge

Answer 21

Well, equation (2) x+y=6 is very simple, so would be easy to rewrite as y=(6-x). Then substitute that expression for y, (6-x) into equation (1) thusly:

\[\large 4x+3y=22\rightarrow4x+3(6-x)=22.\]

Solve for x, then go back to equation (2) to get y.

Answer 22

ok thanks for all your help :D