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Modeling and Analyzing Real-World Systems in 8th Grade

Authored by Anthony Clark

English, Mathematics

8th Grade

CCSS covered

Modeling and Analyzing Real-World Systems in 8th Grade
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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A farmer has 100 feet of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write a system of equations to represent the perimeter. Graph the equations and find the dimensions that maximize the area.

Length: 25 feet, Width: 25 feet

Length: 30 feet, Width: 20 feet

Length: 50 feet, Width: 5 feet

Length: 40 feet, Width: 10 feet

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A school is selling tickets for a concert. Adult tickets cost $10 and student tickets cost $5. If the school wants to raise $500, write a system of equations to represent the number of adult and student tickets sold. Graph the equations and analyze the possible solutions.

5x + 10y = 500, x >= 0, y >= 0

The system of equations is: 10x + 5y = 500, x >= 0, y >= 0.

10x + 5y = 250, x >= 0, y >= 0

10x + 5y = 1000, x >= 0, y >= 0

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 a week, while Jamie saves $10 a week. If Alex starts with $50 and Jamie starts with $30, write a system of equations to model their savings over time. Graph the equations and determine when they will have the same amount saved.

5 weeks

6 weeks

4 weeks

7 weeks

Tags

CCSS.8.EE.C.8C

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A local bakery sells two types of cookies: chocolate chip and oatmeal raisin. The bakery makes a total of 200 cookies each day. If the number of chocolate chip cookies is represented by x and the number of oatmeal raisin cookies by y, write a system of equations to represent the situation. Graph the equations and find the possible combinations of cookies.

x + 2y = 200, where x >= 0 and y >= 0.

The system of equations is: x + y = 200, where x >= 0 and y >= 0.

x - y = 200, where x >= 0 and y >= 0.

x + y = 100, where x >= 0 and y >= 0.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges a flat fee of $20 plus $0.25 per mile. Write a system of equations to represent the total cost for each company. Graph the equations and determine at what mileage the costs are equal.

250 miles

150 miles

300 miles

200 miles

Tags

CCSS.8.EE.C.8C

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A movie theater has two types of tickets: adult tickets for $12 and child tickets for $8. If the theater sells a total of 150 tickets and makes $1,200, write a system of equations to represent the situation. Graph the equations and analyze the solutions to find the number of adult and child tickets sold.

0 adult tickets and 150 child tickets were sold.

100 adult tickets and 50 child tickets were sold.

50 adult tickets and 100 child tickets were sold.

75 adult tickets and 75 child tickets were sold.

Tags

CCSS.8.EE.C.8C

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A gym offers two membership plans. Plan A costs $30 per month with a one-time fee of $50, while Plan B costs $20 per month with a one-time fee of $100. Write a system of equations to model the total cost over time. Graph the equations and determine after how many months the costs will be the same.

5 months

10 months

7 months

3 months

Tags

CCSS.8.EE.C.8C

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