Question

A gas station sells a total of 4500 gallons of regular gas and premium gas in one day. The ratio of gallons of regular gas sold to gallons of premium gas sold is 7 : 2. A. Write

Answer 1

Question is Incomplete; Complete question is given below.

A gas station sells a total of 4500 gallons of regular gas and premium gas in one day. The ratio of gallons of regular gas sold to gallons of premium gas sold is 7 : 2.

a. Write a system of linear equations that represents this situation.

b. How many gallons sold were regular gas? premium gas?

Answer:

a. System of linear equations that represents this situation is
`7x+2x=4500`.

b. 3500 gallons of regular gas and 1000 gallons of premium gas was sold.

Explanation:

Given:

Total Number of gallons of gas sold =4500 gallons.

The ratio of gallons of regular gas sold to gallons of premium gas sold is 7 : 2.

we need to find the amount of regular gas and premium gas sold in gallons.

Solution:

Let the Multiplicative factor be denoted by 'x'.

So Amount of regular gas sold =
`7x`

Amount of premium gas sold =
`2x`

So we can say that;

Total gas sold sold is equal to sum of Amount of regular gas sold and Amount of premium gas sold.

framing in equation form we get;

`7x+2x=4500`

Hence system of linear equations that represents this situation is
`7x+2x=4500`.

On Solving the above equation we get;

`7x+2x=4500\\\\9x=4500`

Dividing both side by 9 we get;

`(9x)/(9)=(4500)/(9)\\\\x=500`

So we can say that;

Amount of regular gas sold =
`7x =7*500 =3500\ gallons`

Amount of premium gas sold =
`2x =2\timees500 =1000\ gallons`

Hence 3500 gallons of regular gas and 1000 gallons of premium gas was sold.