Please Check this word problem for me.

[krisolaw]

How many pounds of extra-lean hamburger that is 7% fat must be mixed with 30 lbs of lean hamburger that is 15% fat to obtain a mixture that is 10% fat?

Here is what I get:
.07x + .15(30-x) = .10
7x + 450 - 15x = 10
-8x = -440
x = 55

It takes 55 pounds of 7% extra-lean hamburger is what I come up with. Please check for me and if I didn't do it right, please explain. Thanks in advance.

 

[tkhunny]

How many pounds of extra-lean hamburger that is 7% fat must be mixed with 30 lbs of lean hamburger that is 15% fat to obtain a mixture that is 10% fat?

.07x + .15(30-x) = .10

Nope. Good try, though.

That 30-x puzzles me. You have 30 lbs. 30-x is less than 30. Don't do that.

x = pounds of 7%

Equating Fat
x*0.07 + 30*0.15 = (30+x)*0.10

Equating Lean
x*0.93 + 30*0.85 = (30+x)*0.90

It doesn't matter on this problem, but for others, if you do it one way or the other it may be easier. This is particularly convenient if you are using either a 100% or a 0% piece.

Try again.

 

[krisolaw]

If following the equating lean formula I get the following:

.07x + 4.5 = 3 + .10x
7x + 450 = 30 + 10x (getting rid of decimals by multiplying by 10)
-3x = -420
x = 140

so is the correct answer 140 lbs of 7%? Just want to make sure I am understanding. Thanks again.

 

[soroban]

Hello, krisolaw!

One small error . . .

If following the equating lean formula I get the following:

0.07x + 4.5 = 3 + 0.10x

7x + 450 = 30 + 10x (getting rid of decimals by multiplying by 10)
. . . no, you multiplied by 100

7x + 450 = 300 + 10x

-3x = -150

x = 50

so is the correct answer 50 lbs of 7%

 

[krisolaw]

Thanks for clearing it up for me... I think I've finally got it. Thanks again.