Cubes and Pyramids

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

Let x = the number of cubes 

      y = the number of pyramids

 

x + y = 17 and so y = 17 - x

6x + 5y = 95

6x + 5(17 - x) = 95

6x + 85 - 5x = 95

x + 85 = 95

x = 95 - 85

x = 10 and so y = 7. (Check : 10 + 7 = 17 and 6(10) + 5(7) = 95)

Answer 2

Let c = the number of cubes

Let p = the number of pyramids

c + p = 17    or    p = 17 - c

6c + 5p = 95

6c + 5(17 - c) = 95

6c + 85 - 5c = 95

c + 85 = 95

c = 10 cubes