System of equations test word problems. I need step by step

Question

Ella is cooking a turkey and a ham. It takes 16 minutes per pound to cook a turkey and 22 minutes per pound to cook a ham.

Ella is able to cook the turkey and the ham in 8 hours and 6 minutes. If the turkey weighs twice as much as the ham, how much do the turkey and the ham weigh?

 A. 

The turkey weighs 18 pounds, and the ham weighs 9 pounds.

 B. 

The turkey weighs 36 pounds, and the ham weighs 18 pounds.

 C. 

The turkey weighs 9 pounds, and the ham weighs 9 pounds.

 D. 

The turkey weighs 9 pounds, and the ham weighs 18 pounds.

Answer 1

Let x – turkey

Let y – ham

To keep our units, the same we need to work in one. We can choose to work in minutes or hours, NOT both. I chose to use minutes. So I need to make sure everything I work in is in minutes:

8 hours = 8* 60 = 480 hours

480 minutes + 6minutes = 486 minutes of total cook time

16 minutes per pound of turkey or 16x

22 minutes per pound of ham or 22y

Between the two, the total time is 486

So we combine the two to get our equation: 16 x + 22 y = 486

Turkey is twice as much as the ham ---- x = 2y ( 2 times the ham = 1 times the turkey)

How much does each weigh? We have two equations and two variables so we can solve this in several ways.

Let’s solve for one variable 1^st --- we are already given one in terms of the other … x=2y

So we are given weights so we just need to plug them into either of equations and see if they work, meaning they are equal on side of the equation and the other when we plug in the given values

Let us start with A and plug in these values. We can use either equation 1 or 2. In this case I picked equation 2.  

Let 18 pounds of turkey be x and 9 pounds of ham be y….

x = 2y = --> 18 = 2*9  --> 18 = 18 ?? yes that works. Answer A is valid this far.  

So let us plug B into our 2^nd equation

x = 2y --> 36 = 2*18 --> 36 =36 Answer B is valid.

Plug in C to our 2^nd equation

x= 2y --> 9 = 2*9 ---> 9 does not equal 18 Answer C is not valid

Plug in D to our 2^nd equation

X = 2y --> 9 = 18 *2 à 9 does not equal 36 Answer D is not valid