Word problem Guide 3, 5th ed, page 57, A mixture of "lean"

[heggyy]

A mixture of "lean" ground beef (10% fat) and "super-lean" ground beef (3% fat) has a total fat content of 8%. What is the ratio of "lean" ground beef to "super-lean" ground beef?

Why X(2) + Y(-5) = 0?
I don't understand how both differentials multiply by different numbers equals zero.

Thank you!

[tim]

this is all explained in our strategy guide. can you be more specific about exactly what you didn't understand in the strategy guide?

[heggyy]

I don't understand the logic why the differentials multiply by two numbers should equal to Zero. Could you explain that?

[RonPurewal]

A mixture of "lean" ground beef (10% fat) and "super-lean" ground beef (3% fat) has a total fat content of 8%. What is the ratio of "lean" ground beef to "super-lean" ground beef?

Why X(2) + Y(-5) = 0?
I don't understand how both differentials multiply by different numbers equals zero.

Thank you!

the idea is that the total amounts over and under the weighted average have to equal out. (if there's more "over" than "under", or vice versa, then that's not actually an average.)

if the weighted average is 8%, then the "over" amount (the 10%-fat ground beef) is 2% over, hence the +2. likewise, the "under" amount (the 3%-fat beef) is 5% under, hence the negative 5.

if you don't like the negative signs, you can just write an equality with the "overs" on one side and the "unders" on the other side:
overs = unders
2(x) = 5(y) [where x and y are the amounts of 10%- and 3%-fat beef, respectively]
this is the same as the equation you've listed, except without the negative sign.

--

lastly, if this still doesn't make sense to you, it's not really necessary anyway. it's a nice auxiliary shortcut, but, you can always just solve the problem with the traditional algebra for weighted averages: 0.10x + 0.03y = 0.08(x + y), then solve for the ratio of x to y.

[heggyy]

Makes sense. :)

[tim]

:)