# The volume of a rectangular parallelepiped is 84 cm3. This parallelepiped was divided into two parts.

**The volume of a rectangular parallelepiped is 84 cm3. This parallelepiped was divided into two parts. find the volume of each part if: a) the volume of one part is 6 times the volume of the other; b) the volume of one part is 40 cm3 more than the volume of the other part.**

a) Let the volume of the first part of the parallelepiped be x cm ^ 3, then the volume of the second part is 6x cm ^ 3.

x + 6x = 84;

7x = 84;

x = 84/7;

x = 12.

If x = 12, then the volume of the first part is 12 cm ^ 3, and the second is 72 cm ^ 3.

Answer: 12 cm ^ 3 and 72 cm ^ 3.

b) Let the volume of the first part of the parallelepiped be x cm ^ 3, then the volume of the second part is (x + 40) cm ^ 3.

x + x + 40 = 84;

2x = 84 – 40;

2x = 44;

x = 22.

If x = 22, then the volume of the first part is 22 cm ^ 3, and the second is 62 cm ^ 3.

Answer: 22 cm ^ 3 and 62 cm ^ 3.