FOIL with division? (350x+4400)/(16+x)=300

[ALZ]

I have this problem: (350x+4400)/(16+x)=300. It is the equation I got from this word problem:

"There are 16 pounds of Tea B, worth 2.75 a pound. How many pounds of Tea A, worth 3.50 a pound, must be added to make a mixture worth 3.00 a pound?"

I know FOIL, but what about two binomials in division? Thanks in advance.

 

[galactus]

YOu don't need FOIL.

\(\displaystyle \L\\2.75(16)+3.5x=3(16+x)\)

 

[skeeter]

(350x+4400)/(16+x) = 300

multiply both sides by (16+x) ...

350x+4400 = (16+x)300

distribute the right side, combine like terms, and solve for x.


FOIL? :?

 

[ALZ]

So then...applying the distributive property...it becomes 44+3.5x=48+3x... equals 3.5x=3x+4... 0.5x=4...x=8! But then 3.50(8)+16(2.75)/16+8...doesn't equal 3.00. SO, three questions: what did I do wrong (if anything)?, what did you do to reach the equation you posted, and how do you do FOIL with division? Thanks! Hopefully you're not annoyed by my abnormally slow brain :winkfor Galactus)

 

[ALZ]

I did skeeter's way, and x does equal 8. I plugged 8 into the original problem, and it still came out as 2.75 no matter how many times I did it. Is there anything wrong with my previous equation?

 

[skeeter]

So then...applying the distributive property...it becomes 44+3.5x=48+3x... equals 3.5x=3x+4... 0.5x=4...x=8! But then 3.50(8)+16(2.75)/16+8...doesn't equal 3.00.

you're right ... 3.50(8)+16(2.75)/16+8 does not equal 3, but

[3.50(8)+16(2.75)]/(16+8) does equal 3.