how many three-quarter pound burgers can be made with twelve pounds of hamburgers

Question

The teacher says 9 is wrong.

Answer 1

As previously stated your initial mistake was in multiplying

instead of dividing the 12 and the 3/4

 

Look at the units.

 

We need to end up with burgers

We have pounds and pounds per burger  Or  P and P/B

 

To end up with Burgers ..B   divide P by P/B 

P/(P/B) = P(B/P) = B

This means if you divide the pounds by the pounds per burger

you get the number of burgers

 

12/(3/4) = 12(4/3) = 4(4) = 16 burgers

Answer 2

12 pounds divided by 3/4 pound, so 12/.75

Answer 3

Ok, 9 is wrong because you got 9 by multiplying 3/4 x 12.  Sometimes using units helps.  I'm going to change 3/4 to .75, and I'm going to set this up like a proportion that is saying is .75 lbs is used for 1 hamburger, I will use 12 lbs for how many hamburgers.

 

That looks like this:

 

.75 lbs = 12 lbs

1 HB         x HB

 

When I cross multiply, I get:

 

(.75 lbs)(x HB) = (12 lbs)(1 HB)    

 

That turns into:

 

(.75 lbs)(x HB) = 12 lbs HB

 

I divide by .75 lbs:

 

x HB = 12 lbs HB/ .75 lbs

 

x HB = 16 HB

 

The problem was that you were multiplying by 3/4 or .75, when you needed to be dividing by 3/4 or .75.

 

Good luck:)