Given parameters:
First term of the sequence = x
Second term = x + 2
Third term = x + 4
Sum of the first three terms = 72
Unknown:
First term of the sequence = ?
Solution:
The sum of the first three terms is unknown;
(x) + (x + 2) + (x + 4) = 72
Solve for x;
x + x + 2 + x + 4 = 72
3x + 6 = 72
3x = 72 - 6
3x = 66
x = = 22
The first term of the sequence is 22
Answer:
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)
Part d) see the explanation
Step-by-step 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
Solve for x
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
