Question

A container is 1/10 full of grain. If 21 additional gallons of grain are added, the container is 4/5 full. What is the volume of the container, in gallons?

Answer 1

30 gallons

Explanation:

let x represent the full container, then

`(1)/(10)` x + 21 =
`(4)/(5)` x

Multiply through by 10 to clear the fractions

x + 210 = 8x ( subtract x from both sides )

210 = 7x ( divide both sides by 7 )

30 = x

The volume of the container is 30 gallons

Answer 2

Answer: the volume of the container is 30 gallons

Explanation:

Let V represent the volume of the container, in gallons.

The initial volume of grains in the container is 1/0 × V = V/10

If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore

4/5 × V = 21 + V/10

4V/5 = 21 + V/10

4V/5 - V/10 = 21

7V/10 = 21

Multiplying the left hand side and right hand side of the equation by 10, it becomes

7V/10 × 5 = 21 × 10 = 210

7V = 210

V = 210/7 = 30