Write a system of equations for the situation and determine how many cookies of each kind were sold. - Explain and Show Work

Question

Bogan High School students were selling cookies as part of a school fundraiser. Cookies were $4 for Chocolate Chip and $5 for Nutella Filling. They ended up raising $1,000 in ticket sales by selling a total of 230 cookies. Write a system of equations for the situation and determine how many cookies of each kind were sold.

Answer 1

Let

 

Number of Chocolate Chip cookies= x

 

Number of Nutella Filling cookies =y

 

Total number of cookies 

x+y=230

 

Fund raise by selling chocolate cookies = 4x

 

Fund raise by selling Nutella Filling cookies=5y

 

4x+5y= 1000

 

so here we got 2 equations

 

x+y=230 --------------------equation 1

 

4x+5y=1000 ---------------equation   2

 

multiply equation 1 with -4

-4x-4y= -920

add these 2 equation

 

-4x-4y=-920

4x+5y=1000

--------------------------

      y= 80

so x= 150

 

Nutella Filling cookies= 80

 

Chocolate Chip cookies= 150

 

Answer 2

we assume the the sold chocolate chip is x, the Nutella is y

 

4x + 5y = 1000      this is equation 1

 x + y = 230          this is equation 2

 

use the substitution x = 230 - y and put it into equation 1

 

4(230 - y) + 5y = 1000

  920 - 4y + 5y  = 1000

                     y = 1000 - 920 

                     y = 80

 

x = 230 - y = 230 - 80 = 150 

 

150  chocolate chip, 80  Nutella  were sold