John is makinga 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.

Question

johnweldon1993 · Answer

Alright so the total OUNCES he wants from a mixture of both...is 6

Let strawberry = s and banana = b

s + b = 6

We also know there are 4 grams per ounce in the strawberry and 3 grams per ounce of the banana...and he wants a total of 22 grams of protein...so

4s + 3b = 22

We have a system of equations here


s + b = 6
4s + 3b = 22

johnweldon1993 · Answer

Do you know how to solve these types of problems?

anonymous · Answer

yes  you just replace the s with 3 and the b with 3, right?

johnweldon1993 · Answer

Not quite

johnweldon1993 · Answer

We want to solve that top equation for 's'

anonymous · Answer

ohhh..

johnweldon1993 · Answer

so 

s + b = 6

s = 6 - b

Now we plug that in for 's' in our second equation

4s + 3b = 22

becomes

4(6 - b) + 3b = 22
24 - 4b + 3b = 22
-b = -2
b = 2

So this means he wants 2 ounces of banana

And if he wants 2 banana...he wants

s + b = 6
s + 2 = 6
s = 4

he would want 4 ounces of strawberry...

And to check...plug b = 2 and s = 4 into equation 2


4s + 3b = 22

4(4) + 3(2) = 22

16 + 6 = 22

22 = 22 $\large \checkmark$

anonymous · Answer

ok

anonymous · Answer

how do you get -b

johnweldon1993 · Answer

s + b = 6

We wanted to solve this...for 's' ....because we wanted to be able to plug in something for 's' in the second equation..

so I subtracted 'b' from both sides...this made 's' alone on the left side and gave us

s = 6 - b

anonymous · Answer

ok thank you

johnweldon1993 · Answer

No problem!