Systems of Equations Word Problems 2

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 5

What are the values of the pronumerals

$x$ and

$y$ ?

$x=$ (45) $cm$

$y=$ (35) $cm$

Question 2 of 5

Find the value of the base angles

$\text(Base Angle) =$ (70) $°$

Question 3 of 5

3. Question
A stack of $37$ coins consisting of $10$ cents and $50$ cents adds up to $$9.70$ . How many $10$ cent and $50$ cent coins are there?
- $10 \text(cents)=$ (22)
  
  $50 \text(cents)=$ (15)
Hint

Help Video
Correct

Well Done!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First, let $x$ be the number of $10$ cents coins and $y$ be the number of $50$ cents coins

Use these values to create a systems of equations

$50$ $x$ $+50$ $y$ $=$ $970$ Total value of coins

$x$ $+$ $y$ $=$ $37$ Number of coins

Multiply equation $2$ by $10$

$($ $x$ $+$ $y$ $)$ $xx10$ $=$ $37$ $xx10$

$10$ $x$ $+10$ $y$ $=$ $370$

Subtract the transformed equation from the first equation.

$10$ $x$ $+50$ $y$ $=$ $970$

$10$ $x$ $+10$ $y$ $=$ $370$

$40y$ $=$ $600$

$y$ $=$ $15$ Divide both sides by $40$

Solve for $x$ .

$x$ $+$ $y$ $=$ $37$

$x$ $+$ $15$ $=$ $37$ Substitute $y=15$

$x+15$ $-15$ $=$ $37$ $-15$ Subtract $15$ from both sides

$x$ $=$ $22$

$x =22$ , $y=15$
Question 4 of 5

4. Question
Jason is three times as old as his son Peter. The sum of their ages is $64$ . What are their ages?
- Peter's age $=$ (16)
  
  Jason's age $=$ (48)
Hint

Help Video
Correct

Fantastic!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First, let variables to represent the age of Peter and Jason.

$x=$ Peter’s age

$y=$ Jason’s age

Next, write the systems of equations being represented in the problem.

$y$ $=$ $3$ $x$ Jason is three times as old as Peter.

$x$ $+$ $y$ $=$ $64$ The sum of their ages is $64$

Substitute Equation $1$ into $2$ and solve for Peter’s age $(x)$ .

$x$ $+$ $y$ $=$ $64$

$x$ $+$ $3x$ $=$ $64$ $y=3x$

$4x$ $=$ $64$

$x$ $=$ $16$ Divide both sides by $4$

Solve for Jason’s age $(y)$ .

$y$ $=$ $3$ $x$

$y$ $=$ $3$ $(16)$ Substitute $x=16$

$y$ $=$ $48$ Simplify

Peter’s age is $16$ while Jason is $48$ years old.
Question 5 of 5

5. Question
Find the value of $x$ and $y$
- $x=$ (20) $°$
  
  $y=$ (30) $°$
Hint

Help Video
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

First, recall that supplementary angles are equal to $180°$

Equate the values of the two lower angles to $180°$ and simplify

$3x+2y+3x$ $=$ $180$

$6x+2y$ $=$ $180$ Combine like terms

Next, recall that alternate angles are equal

Equate the alternate angles and simplify

$2y$ $=$ $3x$

Next, write the systems of equations being represented in the problem.

$6$ $x$ $+2$ $y$ $=$ $180$ First equation

$2$ $y$ $=$ $3$ $x$ Second equation

Substitute the value of $2y$ into Equation $1$ and solve for $x$ .

$6$ $x$ $+2$ $y$ $=$ $180$

$6$ $x$ $+$ $3x$ $=$ $180$ $2y=3x$

$9x$ $=$ $180$

$x$ $=$ $20°$ Divide both sides by $9$

Solve for $y$ .

$2$ $y$ $=$ $3$ $x$

$2$ $y$ $=$ $3$ $(20)$ Substitute $x=20$

$2y$ $divide2$ $=$ $60$ $divide2$ Divide both sides by $2$

$y$ $=$ $30°$

$x =20°$ , $y=30°$

$5$ $x$ $+2$ $y$	$=$	$295$	Length
$3$ $x$ $+4$ $y$	$=$	$275$	Width

$(5$ $x$ $+2$ $y$ $)$ $xx2$	$=$	$295$ $xx2$
$10$ $x$ $+4$ $y$	$=$	$590$

$10$ $x$ $+4$ $y$	$=$	$590$
$3$ $x$ $+4$ $y$	$=$	$275$

$7x$	$=$	$315$
$x$	$=$	$45 cm$	Divide both sides by $7$

$3$ $x$ $+4$ $y$	$=$	$275$
$3$ $(45)$ $+4$ $y$	$=$	$275$	Substitute $x=45$
$135+4y$ $-135$	$=$	$275$ $-135$	Subtract $135$ from both sides
$4y$	$=$	$140$	Divide both sides by $4$
$y$	$=$	$35 cm$

$3x-17$	$=$	$x+y$
$3x-17$ $-x$	$=$	$x+y$ $-x$	Subtract $x$ from both sides
$2x-17$ $+17$	$=$	$y$ $+17$	Add $17$ to both sides
$2x$ $-y$	$=$	$y+17$ $-y$	Subtract $y$ from both sides
$2x-y$	$=$	$17$

Systems of Equations Word Problems 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Excellent!

2. Question

Hint

Nice Job!

3. Question

Hint

Well Done!

4. Question

Hint

Fantastic!

5. Question

Hint

Great Work!

Quizzes

$3x-17+x+y+40$	$=$	$180$
$4x+y+23$	$=$	$180$	Combine like terms
$4x+y+23$ $-23$	$=$	$180$ $-23$	Subtract $23$ from both sides
$4x+y$	$=$	$157$	Subtract $y$ from both sides

$2$ $x$ $-$ $y$	$=$	$17$	First equation
$4$ $x$ $+$ $y$	$=$	$157$	Second equation

$2$ $x$ $-$ $y$	$=$	$17$
$2$ $(29)$ $-$ $y$	$=$	$17$	Substitute $x=29$
$58-y$ $-58$	$=$	$17$ $-58$	Subtract $58$ from both sides
$-y$ $times(-1)$	$=$	$-41$ $times(-1)$	Multiply both sides by $-1$
$y$	$=$	$41$

$x$ $+$ $y$	$=$	$29$ $+$ $41$	Substitute known values
	$=$	$70°$

$3$ $x$ $-17$	$=$	$3$ $(29)$ $-17$	Substitute known values
	$=$	$87-17$
	$=$	$70°$

$50$ $x$ $+50$ $y$	$=$	$970$	Total value of coins
$x$ $+$ $y$	$=$	$37$	Number of coins

$($ $x$ $+$ $y$ $)$ $xx10$	$=$	$37$ $xx10$
$10$ $x$ $+10$ $y$	$=$	$370$

$10$ $x$ $+50$ $y$	$=$	$970$
$10$ $x$ $+10$ $y$	$=$	$370$

$40y$	$=$	$600$
$y$	$=$	$15$	Divide both sides by $40$

$x$ $+$ $y$	$=$	$37$
$x$ $+$ $15$	$=$	$37$	Substitute $y=15$
$x+15$ $-15$	$=$	$37$ $-15$	Subtract $15$ from both sides
$x$	$=$	$22$

$y$	$=$	$3$ $x$	Jason is three times as old as Peter.
$x$ $+$ $y$	$=$	$64$	The sum of their ages is $64$

$x$ $+$ $y$	$=$	$64$
$x$ $+$ $3x$	$=$	$64$	$y=3x$
$4x$	$=$	$64$
$x$	$=$	$16$	Divide both sides by $4$

$6$ $x$ $+2$ $y$	$=$	$180$	First equation
$2$ $y$	$=$	$3$ $x$	Second equation

$6$ $x$ $+2$ $y$	$=$	$180$
$6$ $x$ $+$ $3x$	$=$	$180$	$2y=3x$
$9x$	$=$	$180$
$x$	$=$	$20°$	Divide both sides by $9$