the farm picked 194 Granny Smith apples and 108 Golden Delicious apples. How many pies and jars of applesauce can the farm make if every apple is used?

Question

pie: 5 granny smith apples and 3 Golden delicious apples

applesauce: 6 granny smith apples and 3 golden delicious apples

Answer 1

If we begin by looking at the Granny Smith apples, we can say that

 

5 apples per pie and six apples per applesauce has to equal 194 apples

 

So 5p + 6s = 194.

 

We can then look at the Golden Delicious apples, and say that

 

3 apples per pie and 3 apples per applesauce has to equal 108 apples

 

So 3p + 3s = 108

 

Now we just have to solve these two equations...        let's double the Golden Delicious and subtract the Granny Smith

 

6p + 6s = 216         - (5p + 6s = 194)

 

which is the same as    (6p - 5p) + (6s - 5s) = (216 - 194)

 

so if I do the subtractions, p = 22.

 

Then, substituting back into Golden Delicious,   (3 * 22) + 3s = 108

 

  3s = 108 - (3 * 22) = 108 - 66 = 42

 

   s = 42/3  = 14

 

And if I make 22 pies, I will have enough apples for exactly 14 jars of applesauce.