Respuesta :
Answer:
The cost of the gas per gallon is $2.1 and the cost of the car wash is $6.
Step-by-step explanation:
Given the cost of the gas per gallon is [tex]x[/tex] dollars. And the charge of car wash is [tex]y[/tex] dollars.
Also, it was given that two cars fill up their tank and go for a car wash. We can write linear equation for each case.
One car pays $22.80. It uses 8 gallons gas and go for car wash.
[tex]22.80=8x+y[/tex] Equation (1)
The other car pays $18.60. It uses 6 gallons gas and go for a car wash.
[tex]18.60=6x+y[/tex] Equation (2)
[tex]y=18.60-6x[/tex] substitute this value of [tex]y[/tex] in equation (1) we get,
[tex]22.80=8x+18.60-6x\\22.80=2x+18.60\\22.80-18.60=2x\\4.2=2x\\x=\frac{4.2}{2}=2.1\\ x=2.1[/tex]
Now, to find the value of [tex]y[/tex] we will plug value of [tex]x=2.1[/tex] in [tex]y=18.60-6x[/tex]
[tex]y=18.60-6x\\y=18.60-6(2.1)\\y=18.60-12.6\\y=6[/tex]
So, the cost of the gas per gallon is $2.1 and the cost of the car wash is $6.
