Simultaneous equations

Question

A gas station sells three types of gas: Regular for $3.12 a gallon, Plus for $3.25 a gallon,
and Premium for $3.49 a gallon. On a particular day, 4068 gallons of gas were sold for a total of $13,051.60.
If four times as many gallons of Regular were sold as Premium, how many gallons of each type of gas were
sold that day? When solving this problem, be sure to label any variables that you’ve chosen and clearly
write out the system of equations that you plan to use

Answer 1

Let x denotes the amount of Regular gas ($3.12 per gallon

y Plus ($3.25 per gallon) and z Premium ($3.49 a gallon) then

x+y+z=4068

3.12 x+3.25 y+3.49 z=13,051.60

x=4z

Now you have to solve this system of equations. or equivalently, after substitution x=4z, the system

y+5z=4068

325 y+1597 z=1305160

x=4z

The answer is

x= 2420, y= 1043, z  605