how to solve

Question

a box contains both cubes and five-sided pyramids. The total number of objects in the box is 17. The total number of sides for the cubes and pyramids is 95. How many cubes are in the box?

Answer 1

A cube has 6 sides.

 

The number of sides for all of each object = (number of sides)*(number of objects)

 

Let:

   C = number of cubes

   P = number of pyramids

 

Translate:

  "total number of objects in the box is 17"   means    C + P = 17  [eq1]

  "total number of sides for the cubes and pyramids is 95"    means

                                              6C      +     5P        =  95      [eq2]

 

You may use either substitution or elimination.  Let's do elimination:

    6C  +  5P  = 95     [eq2 again]

    5C  +  5P  = 85     [5*eq1]

 ---------------------  [elimination; subtract equations]

     C            = 10

 

There are 10 cubes in the box.

 

Checking:  C+P=17, so P=7.

   Does   6(10) + 5(7) = 95   ?

               60    +  35  = 95   ?

                     95 = 95   ?yes

Answer 2

c represents the number of cubes

p represents the number of pyramids

 

c + p = 17          sum of objects

6c + 5p = 95      sum of sides

 

Can you solve this system?