Adrian, Dakota and Calvin made an average of 52 snacks.

Question

Adrian and Dakota made an average of 61 snacks. Dakota and Calvin made an average of 44 snacks. How many snacks did each of them make?

Answer 1

A = Average of snacks made by Adrian

D = Average of snacks made byDakota

C = Average of snacks made byCalvin

 

These are averages, so you need to add the individual rates and divide by the number of entries. Then work the system of equations.

 

A+D+C = 52               A+D = 61            D+C = 44

    3                              2                         2

 

A+D+C=52(3)            A+D = 61(2)       D+C = 44(2)          Now solve in terms of the common variable of the last two

A+D+C=156               A+D = 122         D+C = 88                    equations. That being the D.

                                  A= 122-D           C = 88-D               Now substitute these values into the first equation.

 

(122-D)+D+(88-D)=156                                                    And now you have only one variable the D. Solve:

122+88-2D+D=156

         210 - D = 156

                -D = -54

                 D = 54

 

Now substitute in D to solve for the other values.

 

A+D = 122                  D+C=88

A+54= 122                 54+C=88

     A = 68                       C = 34

 

Check:

 

A+D+C = 52      68 + 54 + 34 = 52
   3                            3

 

                               156  = 52

                                 3    

  

                                52 = 52   √

 

Adrian averaged 68 snacks        

Dakota averaged 54 snacks

Calvin averaged 34 snacks