math question help

Question

Greg's gas tank is 1/6 full. After he buys 11 gallons of gas, it is 2/3 full. How many gallons can Greg's tank hold?

Answer 1

Let x equal the number of gallons the gas tank holds.

Initially the tank holds (1/6)x.

Then 11 gallons are added, so now the tank holds:

(1/6)x + 11

But that amount is two-thirds of a full tank. That means the following equation models the situation:

(1/6)x + 11 = (2/3)x

To solve that equation for x, probably easiest to multiply every term by 6 (LCD) to clear the equation of fractions:

x + 66 = 4x [hopefully you see that 6 (1/6) x = x and 6(2/3)x = 4x]

66 = 3x

x = 22 gallons in a full tank.

Check:

(1/6)(22) + 11 =? (2/3)(22)

11/3 + 33/3 =? 44/3

44/3 = 44/3