A fast food restaurant has 25% fat hamburger meat and 15% fat hamburger meat.

Question

This is  the complete question:

A fast food restaurant has 25% fat hamburger meat and 15% fat hamburger meat. How many pounds of each type of meat should be mixed to make 90 lb of hamburger meat that is 18% fat?

Answer 1

 X - lb of 25%

 90 - X = amount of 15%

 

    X ( 0.25) + ( 90-x) ).15 = 90( 0.18

 

       0.10 X = 90( 0.03)

 

            X = 2.7 / 0.10 = 27 lb  25% Hamburger

 

             90- 27 = 63 lb     15% Hamburger.   

Answer 2

A fast food restaurant has 25% fat hamburger meat and 15% fat hamburger meat. How many pounds of each type of meat should be mixed to make 90 lb of hamburger meat that is 18% fat?

 

The mixture will be 90 lb, and contain 18% fat, or 16.2 lbs of fat, leaving 73.8 lbs meat.

 

So, we can use these two equations, where x represents the amount of 25% meat, and y represents the amount of 15% meat:

 

.25x + .15y = 16.2

x + y = 90

 

Taking the second equation, subtract y from both sides:

 

x = -y + 90

 

Substitute this value for x back into the first equation:

 

.25(-y + 90) + .15y = 16.2

 

Using distributive property to remove parentheses:

-.25y + 22.5 + .15y = 16.2

 

-.1y + 22.5 = 16.2

 

Subtract 22.5 from both sides:

 

-.1y = 16.2 - 22.5

-.1y = -6.3

 

Multiply both sides by -10:

y = 63

 

Plug this value back into the second equation:

x + y = 90

x + 63 = 90

x = 27

 

So, the mixture should contain 27 pounds of 25%, and 63 pounds of 15%.

 

Let's check our work:

(27 lbs * .25) + (63 lbs * .15) =  6.75 + 9.45 = 16.2 lbs of fat

The total weight is 90 lbs (27 + 63).

Answer 3

Set the problem up as a proportion where percentages as shown as decimals (18% = 0.18).

 

We consider two variable sets of unknowns 

 

x = # of LBS

90- x = # of LBS from 90

 

0.18 * 90 lbs = 0.25* (90-X) + 0.15 * X

 

Solve for X 

 

0.18 * 90 = 0.25*90 - 0.25 * X + 0.15 * X

16.2 = 22.5 - 0.1*X

16.2 - 22.5 = -0.1*X

-6.3 = -0.1 *X

X = 63 lbs of meat

 

Since the X value corresponded to the 0.15 (15% meat) then there should be 63 lbs of 15% meat. 

 

90 lbs - 63 lbs (of 15% meat) = 27 lbs remaining

 

I.E the answer is 27 LBS of 25% Fat Hamburger and 63 LBS of 15% Fat Hamburger.