find the cost of one blueberry pie and one pumpkin pie

Question

jacob and perry are selling blueberry and pumpkin pies. jacob sold 1 blueberry pie and 8 pumpkin pies for $164. perry sold 13 blueberry pies and 4 pumpkin pies for $132. find the cost of one blueberry pie and one pumpkin pie

Answer 1

This kind of problem always leads to a system of two linear equations in two unknowns.  Learn the method I'll describe, because it will apply to many similar problems in the future.

 

Let the selling price of blueberry pies be b, and pumpkin pies use p for selling price.

1b + 8p = 164

13b + 4p = 132   I assume that you can solve this system.

 

The answer will be b = 4  p = 20...Four and twenty (reminds me of the numbers in a nursery rhyme--but that was blackbirds)

 

 

Answer 2

You can solve this using systems of equations. Essentially, modeling both peoples purchases with equations and solving for one variable at a time. Use the general form number of blueberry pies(price of blueberry pies)+number of pumpkin pies(Price of pumpkin pies)=total amount spent.

 

let b= price of blueberry pies

let p= price of pumpkin pies

 

Jacob: 1b+8p=$164

 

Perry: 13b+4p=$132

 

Solve:

 

   1b+8p=164

+(13b+4p=132)

 

         1b+8p=164
+(-2)(13b+4p=132)  You multiply this by negative two so the pumpkin pies will cancel out when you add the equations                                   together

 

     1b+8p=164
+(-26b-8p=-264)  

 

     1b+8p=164
+(-26b-8p=-264)   Now simply add like variables. The pumpkin pies will cancel and you will be left with one variable.

    -25p=-100

 

-25b=-100 

 

-25b/-25=-100/-25 solve for b by dividing both sides by -25

 

b=$4.00

 

1b+8p=164 plug in b for the first equation

 

1(4.00)+8p=164 

 

4.00+8p=164        Solve for p. Start by subtracting 4.00 from both sides.

-4.00       -4.00

8p=160

 

8p/8=160/8    Divide both sides by 8.

p=$20.00

 

Pumpkin pie= $20.00

Blue berry pie= $4.00

 

To check your answer you can plug the values into either of the first equations and it should work:

 

Perry 13(4.00)+4(20.00)=132

Jacob 1(4.00)+8(20.00)=164