A box contains cubes and 5-sided pyramids with 17 items and 95 sides, how many cubes in the box?

Question

A box contains cubes and 5-sided pyramids with a total of 17 items and 95 sides,  How many cubes are in the box?

Answer 1

Cubes have 6 sides and 5 - sided pyramids.

Total items = 17.

Cubes + pyramids = 17

Let be the cubes ( c ) , pyramids ( p )

c + p = 17 ----------> ( 1 )

Total sides = 95

6c + 5p = 95 ----------> ( 2 )

( 1 ) * 6   ⇒  6c + 6p = 102 ----------> (3 )

From (2) & (3)

6c + 5p = 95

6c + 6p = 102

-----------------      ( changing the symbols)

      - p = - 7

Therefore p = 7

Substitute the p value in eq (1)

c + p = 17

c+ 7 = 17

c = 17 - 7 = 10

c = 10

Pyramids = 7

Cubes = 10

Solution :  10 cubes are in the box.