T'dah needed new school supplies. Notebooks cost $3 and a pack of
pencils $1. She has $50 to spend on supplies. Sales tax in Indiana
where she plans to buy her supplies is 7%.
Part A
Write an inequality to represent the number of each item she could
purchase including sales tax and stay in her budget. Be sure to
define the variables you are using for your inequality.
Define your variables:_________
Inequality:___________
Part B
She plans to purchase 11 notebooks and 6 packs of pencils. Can
T'dah make this purchase and stay within her budget?
The table shows the price p for staying in a hotel for d days.
1 80
2 120
3 160
4 200
Part A
Construct. Linear function that models the relationship between the
P, and the number of days, D for which you stay in the room. Show
the steps required to construct the model.
Part B
What does the slope represent in the context of the problem.
Part C
What is the value of the problem when D=0? What does this value
represent in the context of the problem?
The following graph represents the amount of money, d what you
owe on your car after m months.
What is the slope of this graph? What does this slope represent in
the context of the problem?
Write an equation based on the graph that would represent the
money owed, D, after m months.
After how many months will you have your phone paid off? Show
all steps required to get to your answer.
You want to start a t-shirt selling business. You can sell a shirt for
$12. The following graph represents the money made in your
business.
What is the slope of the graph? What does the slope represent in the
context of the problem?
Why does the graph start below the x axis? What would that mean
in the context of the problem?
What is the break even point? What does this mean in the context of
this problem?
Write an equation in slope intercept form to represent how many tshirts, x, you must sell to make y money. Show all work required to
find your answer.
A student earns $7.50 per hour at her part time job. She wants to
earn at least $200.
Enter an inequality that represents all of the possible numbers of
hours (h) the student could work to meet her goal.
Enter the least whole number of hours the student needs to work in
order to earn at least $200.
Mike earns $6.50 per hour plus 4% of his sales. Enter an equation
for Mike's total earnings, E, when he works x hours and has a total
of y sales, in dollars.
Mike wants to earn at least $500 this month. What is the maximum
number of hours he would work if he sold no cars?
Joe bought a package phone from Value Mart for $45. He pays $55
after sending 100 text messages.
Write an inequality to model the price p(t) as a function of t text
messages.
If this trend continues, what will be the cost for 500 text messages?
If Joe can spend at most $130, how many text messages can he
send?
If he sent 725 text messages, what is the most he spent?
A train travels 250 miles at a constant speed, x, in miles per hour.
Enter an equation that could be used to find the speed of the train, if
the time to travel 250 miles is 5 hours.
What is the speed of the train? Show all work required to reach your
answer.
The formula for the rate at which water is flowing is R=v/t where r
is the rate, v is the volume, and t is the time in seconds for which the
water was measured.
Solve this equation for v. Show all steps required to reach your
solution.
If the water your shower is flowing at a rate of 4 gallons per second
for a minute, how many gallons would pass through the shower?
Systems of Equations
1. You spend $264 on clothes. Shirts cost $24 and pants cost $32. You buy a total of 9 items.
a. Write a system of linear equations that represents this situation.
b. Solve the system by graphing. Interpret your solution.
2. A phone company charges $0.06 per minute for local calls and $0.15 per minute for
international calls. When your bill comes, it states that you accumulated 852 minutes with a
charge of $69.84. Write and solve a system of linear equations to find the number of local and
international minutes used.
3. An exam worth 145 points contains 50 questions. Some of the questions are worth two points
and some are worth five points. How many two point questions are on the test? How many five
point questions are on the test?
Write a linear system of equations that can be used to solve this problem. Solve.
4. The Lakers scored a total of 80 points in a basketball game against the Bulls. The Lakers made
a total of 37 two-point and three-point baskets. How many two-point shots did the Lakers make?
How many three-point shots did the Lakers make?
Write a linear system of equations that can be used to solve this problem. Solve.
5. There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in
all. How many of each animal are there?
6. All 231 students in the Math Club went on a field trip. Some students rode in vans which hold
7 students each and some students rode in buses which hold 25 students each. How many of each
type of vehicle did they use if there were 15 vehicles total?
7. Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to
buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells
forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90
on materials for forks and spoons. They sold the finished products for a total of $147.20. How
many forks and how many spoons did they make last April?
Example: y = -2x
and
y=x+3
1) Does the point (0, 4) make either equation true? Substitute it in and find out.
2) Does the point (2, 5) make either equation true? Explain.
3) Does the point (-1, 2) make either equation true? Explain.
If a point works in both equations of a linear system, then that point must be the
SOLUTION to the linear system. When you solve a linear system you find that one
point makes both equations true.
4) What point is the solution to the system above? ____________
Plot both equations in the same coordinate plane below.
At what point do the two lines intersect? _________
y = -2x and
y=x+3
Nicole is making greeting cards, which she will sell by the box at an arts fair. She paid $30 for a
booth at the fair, and the materials for each box of cards cost $6. She will sell the cards for $9 per
box of cards. At some point, she will sell enough cards so that her sales cover her expenditures.
How much will the sales and expenditures be?
Write a system of equations, graph them, and type the solution.