Algebra 1 Systems of Equations- Word Problems

Systems of Equations- Word Problems

Writing Equations

Objective: In this lesson you will learn how to read a systems of equations word problem in context and create two linear equations that represent the given situation.

​Step 1: Read the problem carefully

​I've highlighted the two important sentences.

​Step 2: Analyze the sentences and create two linear equations.

​The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote.

g = 2d-8

They wrote a total of 46 songs.

g + d = 46

"2d" means twice the number of drummer songs

"-8" means eight fewer songs

Multiple Choice

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.

Which system of equations models this situation if the drummer wrote $$d$$   songs and the guitarist wrote $$g$$   songs?

• $$g=2d-8$$  

  $$g+d=46$$  

• $$g=8-2d$$

  $$g=46-d$$

• $$d=2g-8$$

  $$d=46-g$$

• $$d=8-2g$$

  $$d+g=46$$

​Over the next few slides you will have a opportunity to practice building linear expressions from the context of a word problem. The only way to get better at these types of problems is to practice them.

Good luck!

Multiple Choice

The cost of using a cleaning company that charges a flat fee of $40 plus $15 per hour. If $$y$$ represents the total cost and $$x$$ represents the number of hours, which equation best represents the cost of hiring the cleaning company?

• $$y=55x$$

• $$y=40x+15$$

• $$y=15x+40$$

• $$y=45x$$

Match

Match the following situations with the correct algebraic expression.

$$r=$$ number of miles running

$$w=$$ the number of miles walking

• $$r+w=12$$

• $$w=r-12$$

• $$w=12r$$

• $$r=12w$$

• $$r=w-12$$

Esther walked and ran a total of 12 miles.

Gavin walked 12 miles less than he ran.

Grayson walked 12 times as much as he ran.

Brandon ran 12 times as much he walked.

Karla ran 12 miles less than she walked.

• Esther walked and ran a total of 12 miles.

• Gavin walked 12 miles less than he ran.

• Grayson walked 12 times as much as he ran.

• Brandon ran 12 times as much he walked.

• Karla ran 12 miles less than she walked.

Multiple Choice

A university will spend $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250, and each keyboard will cost $50.

 

Which equation represents x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab?

• $$50x+250y=4500$$

• $$250x+50y=4500$$

• $$y=4500-250x$$

• $$x=4500-50y$$

Multiple Choice

A cell phone plan costs $44.50 a month plus $0.40 per minute. If $$y$$ represents the total cost and $$x$$ represents the number of minutes used, which equation best represents the cost of the cell phone plan?

• $$y=.40x$$

• $$y=-.40x+44.50$$

• $$y=44.90x$$

• $$y=.40x+44.50$$

Math Response

An artist bought a set of 10 paintbrushes that contained  $$x$$  small paintbrushes and  $$y$$  large paintbrushes.

Write an equation in standard form $$Ax+By=C$$

 to represent this given situation.

Type answer here

Correct Answer: x+y=10

Deg^°

Rad

Math Response

Last month a mail carrier delivered mail on the morning route 15 times and on the afternoon route 12 times, for a total distance traveled of 150 miles. Let $$x$$ represent the miles of the morning route and $$y$$ represent the number of miles of the afternoon route.

Write an equation in standard form $$Ax+By=C$$

 to represent this given situation.

Type answer here

Correct Answer: 15x+12y=150

Deg^°

Rad

Math Response

An artist bought a set of paintbrushes that contained  $$x$$  small paintbrushes and  $$y$$  large paintbrushes. The number of small paintbrushes in the set was 5 times the number of large paintbrushes in the set. 

Write an equation that represents $$x$$ , the number of small paintbrushes.

Your answer should start with $$x=$$ ____

Type answer here

Correct Answer: x=5y

Deg^°

Rad

Multiple Choice

A mail carrier delivers mail on one of two different routes: a morning route or an afternoon route. Each workday the mail carrier is assigned one of these two routes. 

 

Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times, for a total distance traveled of 141 miles.

This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles.

Which systems of equations can be used to find $$x$$ , the number of miles in the morning and $$y$$ , the number of miles in the afternoon?

• $$12x+16y=141$$

  $$10x+15y=123.75$$

• $$16x+12y=141$$

  $$10x+15y=123.75$$

• $$16x+12y=123.75$$

  $$10x+15y=141$$

• $$16x+12y=141$$

  $$15x+10y=123.75$$

Match

Match the following:

$$x$$ represents the number of cookies

$$y$$ represents the number of brownies

• $$y=2x$$

• $$x+y=15$$

• $$y-x=15$$

• $$y=\frac{1}{2}x$$

• $$y=2x+15$$

There were twice as many brownies as cookies.

There was a total of 15 brownies and cookies.

The difference between the brownies and cookies was 15.

There were half as many brownies as cookies.

The brownies equaled 15 more than twice the number of cookies

• There were twice as many brownies as cookies.

• There was a total of 15 brownies and cookies.

• The difference between the brownies and cookies was 15.

• There were half as many brownies as cookies.

• The brownies equaled 15 more than twice the number of cookies

Multiple Choice

The total amount of the bar depends on how many pairs of weights are added to it. If $$x$$ represents number of plates added and $$y$$ represents the total weight, which equation best represents the given situation?

• $$y=35x+45$$

• $$y=45x+35$$

• $$y=70x+115$$

• $$y=70x+45$$

Poll

How do you feel about system of equation word problems? Are you able to determine the variables? Are you able to find the two "equals"? Are you able to match the equals with an expression?

• I've totally got this!

• I've got this, but still make some calculation errors

• Some I understand, but others totally confuse me.

• I'm lost.