Word Problems
Rob and Shanice each improved their yards by planting rose bushes and shrubs. They bought their supplies from the same store. Rob spent $180 on 6 rose bushes and 10 shrubs. Shanice spent $170 on 11 rose bushes and 5 shrubs. What is the cost of one rose bush and the cost of one shrub?
rose bush $10; shrub $12
What are the steps when solving a system of equations by elimination?
1. Stack you equations so your variables line up in the form Ax+By=C 2. Multiply either equation by any number in order to eliminate one variable, and/or eliminate 1 variable. 3. Solve for the remaining variable. 4. Plug the answer from Step 3 into either equation to solve for the second variable. 5. Write your solution as (x,y) 6. Classify.
What are the steps when solving a system of equations using graphing?
1. Get both equations in slope-intercept form 2. Graph 3. Identify the intersection point 4. Write solution as (x,y) 5. Classify
How do you determine whether to use a solid or dotted line when graphing an inequality?
The inequality sign. If the inequality sign is less or greater than, dotted line. If the inequality sign is less than or equal to, or greater than or equal to, solid line.
Abhasra and Asanji each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Abhasra spent $70 on 5 daylilies and 5 bunches of ornamental grass. Asanji spent $155 on 10 daylilies and 13 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?
daylily $9; bunch of ornamental grass $5
Solve the following system by substitution. You must show your work to earn points.
-5x+8y=-1
y=4x+10
(-3,-2)
Solve and classify the following system of equations using the elimination method. Show your work fully.
x+y=6
2x-y=6
(4,2)
How many solutions does a system in which the 2 equations have the same slope but different y-intercepts have?
None, the lines are parallel so there is no solution.
You have just graphed the inequality y < 5x-5. How do you know whether to shade above or below the line?
Anjali and Jose are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Anjali sold 4 packages of white chocolate chip cookie dough and 12 packages of gingerbread cookie dough for a total of $152. Jose sold 14 packages of white chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $114. What is the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough?
package of white chocolate chip cookie dough: $5, package of gingerbread cookie dough: $11
What is the first step to solve this system of equations using substitution?
8x+8y=-16
-x+y=-4
Isolate y in the second equation by adding x to both sides.
Solve the following system using the elimination method. Show your work fully.
-8x-10y=24
6x+5y=2
(7,-8)
How many solutions does the following system have?
9+x=-3y
-3y-9-x=0
infinitely many solutions
Which point would not be a solution to the system of linear inequalities?
y≥−x+8
y>−2x+2
(8,6)
(12,0)
(2,10)
(-1,1)
The school that Matt goes to is selling tickets to a play. On the first day of ticket sales the school sold 7 senior citizen tickets and 12 child tickets for a total of $99. The school took in $126 on the second day by selling 13 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?
senior citizen ticket: $9, child ticket: $3
Solve the system using substitution. Show your work fully.
x+2y=-6
-3x+5y=-15
(0,-3)
Solve the following system by elimination. Show your work fully.
-3x+7y=-11
7x+7y=-21
(-1,-2)
Solve and classify the following system by graphing: 8x+24y=48
-33y=11x + 33
No solution
Graph the system of inequalities:
y≥x−3
y > −x − 1
Identify one solution an one non-solution.
answers will vary
The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 3 vans and 8 buses with 327 students. High School B rented and filled 1 van and 6 buses with 229 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
van 13, bus 36
Solve the following system using substitution. Show your work fully.
-4x - y=-18
x + 5y=-5
(5,-2)
Solve the system by elimination. Show your work fully.
0=2x+5y-2
28+12x+10y=0
(-4,2)
Write an equation to be added to this system so that the system would have no solutions.
y=-2x+b where b <> 3
An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship a maximum of 32 pieces of furniture and must sell no less than $12000 worth of chairs and tables. Write the system of inequalities and determine one possible solution.
t+c≤32
600t+200c≥12000