Respuesta :
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 [tex]7x+2x=4500[/tex].
b. 3500 gallons of regular gas and 1000 gallons of premium gas was sold.
Step-by-step 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 = [tex]7x[/tex]
Amount of premium gas sold = [tex]2x[/tex]
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;
[tex]7x+2x=4500[/tex]
Hence system of linear equations that represents this situation is [tex]7x+2x=4500[/tex].
On Solving the above equation we get;
[tex]7x+2x=4500\\\\9x=4500[/tex]
Dividing both side by 9 we get;
[tex]\frac{9x}{9}=\frac{4500}{9}\\\\x=500[/tex]
So we can say that;
Amount of regular gas sold = [tex]7x =7\times500 =3500\ gallons[/tex]
Amount of premium gas sold = [tex]2x =2\timees500 =1000\ gallons[/tex]
Hence 3500 gallons of regular gas and 1000 gallons of premium gas was sold.
