Calculating calories

Question

One slice of mincemeat pie has as many calories as six ounces of turkey and a candied yam. If a candied yam has six calories more than four ounces of turkey. Suppose that a slice of mincemeat pie and nine ounces of turkey has 994 calories. How many calories would then be in one candied Yam?

Answer 1

The toughest part is defining our variables since each of the three foods are described in different denominations.  So lets just define them hour they are listed.

 

Let M = the Calories in 1 slice of Mincemeat pie

Let T = the Calories in 6 ounces of Turkey

Let Y = the Calories in 1 Candied Yam

 

Now lets build our three equations required to solve for the 3 variables we defined.

 

We know that M=T+Y

 

The next two equations are more difficult because they require relating to a fraction of our 6 ounce turkey portion.

 

Y=6+T*4/6  (note T*4/6 is the same as 4 ounces of Turkey)

 

M+T*9/6=994  (note that T*9/6 is the same as 9 ounces of Turkey)

 

We now have our three equations for three unknowns.  But before I solve I'm going to rewrite the equations after "clearing" the fractions (ie multiply the entire equation through by the denominator).  The result is

 

M=T+Y     (1)

6Y=36+4T    (2)

6M+9T=5964  (3)

 

Now substitute equations (1) into equation (3)

 

6(T+Y)+9T=5964 

 

which simplifies to

 

15T+6Y=5964

 

Lets rewrite this to get 6Y=5964-15T.  Now I'm going to subtract equation (2) from this result

                                -6Y=-36   -4T

                                   0=5928-19T

 

Solving this for T=312

 

Now I'm going to solve equation (2) for Y (ie candied Yams which is what we are looking for):

 

6Y=36+4T

Y=6+T*4/6

 

Now I can substitute in the value I found for T

 

Y=6+(312)*4/6

Y=6+208

Y=214 Calories

 

So 1 Candied Yam is 214 Calories.

 

Remember if you want to verify this answer you first find M and then subsitute these values into one of the original equations.

 

Good Luck.

 

Cheers

 

-Chris