Question

Scott's gas tank is 1/3 full. After he buys 12 gallons of gas, it is 7/9 full. How many gallons can Scott's tank hold?

Answer 1

Answer: We start with the variable "x". Let's call "x" Dan's full tank.

So we know that right now he has 1/3x or 1/3 of a full tank.

After adding 12 gallons, at the end, he has 7/9x, or 7/9 of a full tank

So we start with

(1/3)x + 12 = 7/9x

Let's subtract 1/3x from both sides

12 = 7/9x - 1/3x

Remember, we need to use common denominators to subtract, so 1/3 becomes 3/9

12 = 7/9x - 3/9x

Now we simplify to get

12 = 4/9x

Multiply the reciprocal of 4/9 to both sides which is 9/4

12 * 9/4 = x

Answer is 27 gallons.