Question

the graph shows your budget and the total cost of x gallons of gasoline and a car wash you want to determine the possible amounts in gallons of gasoline you can buy within your budget. how much does a gallon of gasoline cost? how much does a car wash cost? y=40 and y=3.55x+8

Answer 1

Part a) The budget is $40

Part b) The cost of one gallon of gasoline is $3.55 and the cost of the car wash is $8

Part c)
`x \leq 9.01\ gal`

Part d) see the explanation

Explanation:

The complete question in the attached figure

Part a) What is your budget?

The budget is given by the equation

y=40

therefore

The budget is $40

Part b) How much does a gallon of gasoline cost? how much does a car wash cost?

Let

y ------> the cost of a gallon of gasoline plus the cost of a car wash

x -----> the amount of gasoline in gallons

we have

y=3.55x+8

In this problem

For x=0

y=3.55(0)+8=8

The y-intercept is the cost of the car wash

so

The cost of the car wash is $8

Find the cost of one gallon of gasoline

we know that

The slope of the linear equation is

m=$3.55 per gallon

therefore

The cost of one gallon of gasoline is $3.55

Part c) Write an inequality that represent the possible amounts of gasoline you can buy

we have

`3.55x+8 \leq 40`

Solve for x

`3.55x \leq 40-8`

`3.55x \leq 32`

`x \leq 9.01\ gal`

Part d) Use the graph to estimate the solution of the inequality in part c)

we have the system

y=40

y=3.55x+8

The solution of the system is the intersection point both graphs

Looking at the graph the intersection point is about (9,40)

That means ----> The maximum amount of gasoline you can buy with the budget is about 9 gallons