Question

Amy drives her car until the gas gauge is down to 1/8 full, then she fills the tank to capacity by adding 14 gallons. What is the capacity of the gas tank?

Answer 1

Answer:

Amy's car tank capacity is 16 gallons.

Step-by-step explanation:

Let the capacity of the tank be 'x'

Given:

Amount of gas in the car till it is refilled = $\frac{1}{8}\times x = \frac{1}{8}x \ gallons$

Amount of gas added = 14 gallons.

We need to find the capacity of the tank.

Solution:

Now we can say that

Total Capacity of the tank is equal to sum of Amount of gas in the car till it is refilled and Amount of gas added.

framing in equation form we get;

$x=\frac{x}{8}+14$

Combining the like terms we get;

$x-\frac{x}{8}=14$

Now making the denominators common we will use L.C.M.

$\frac{8x}{8}-\frac{x\times1}{8\times1}=14\\\\\frac{8x}{8}-\frac{x}{8}=14\\\\\frac{8x-x}{8}=14\\\\\frac{7x}{8}=14$

Now multiplying both side by 8 we get;

$\frac{7x}{8}\times 8=14\times8\\\\7x = 112$

Now dividing both side by 7 we get;

$\frac{7x}{7}=\frac{112}{7}\\\\x=16\ gallons$

Hence Amy's car tank capacity is 16 gallons.