Systems of Equations Word Problems 1

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

Sue went shopping on two occasions. On the first occasion she bought

5

$5$ apples and

2

$2$ bananas for $2.80. On the second occasion she paid $5.10 for

3

$3$ apples and

5

$5$ bananas. What is the cost of each fruit?

Apple $= $$ $=$$ (0.20)

Banana $= $$ $=$$ (0.90)

Question 2 of 5

A customer bought

4

$4$ drinks and

3

$3$ pizzas for

$ 40.80

$$40.80$ . Another costumer bought

2

$2$ drinks and

1

$1$ pizza for

$ 15.00

$$15.00$ . Find the price of the following:

$(i)$ $(i)$ A drink: $$$ $$$ (2.10)

$(i i)$ $(ii)$ A pizza: $$$ $$$ (10.80)

Question 3 of 5

$2$ oranges and

$5$ apples cost

$$5.75$ and

$4$ oranges and

$6$ apples cost

$$8.10$ . Find the price of each apple and orange

Orange $=$ (75) $\text(cents)$

Apple $=$ (85) $\text(cents)$

Question 4 of 5

4. Question
At a theatre, there are $400$ patrons. If there were $60$ more women than men, how many men attended the show?
- (170)
Hint

Help Video
Correct

Keep Going!
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 men and women.

$x=$ number of women

$y=$ number of men

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

$x$ $+$ $y$ $=$ $400$ There are a total of $400$ patrons

$x$ $=$ $y$ $+60$ $60$ more women than men

Rewrite equation $2$ such that $x$ and $y$ are on the same side.

$x$ $=$ $y$ $+60$

$x$ $-y$ $=$ $y$ $+60$ $-y$ Subtract $y$ from both sides

$x$ $-$ $y$ $=$ $60$

Add the two equations.

$x$ $+4$ $y$ $=$ $400$

$x$ $-$ $y$ $=$ $60$

$2x$ $=$ $460$

$x$ $=$ $230$ Divide both sides by $2$

Solve for $y$ , the number of men.

$x$ $-$ $y$ $=$ $60$

$230$ $-$ $y$ $=$ $60$ Substitute $x=230$

$230-y$ $-230$ $=$ $60$ $-230$

$-y$ $=$ $-170$

$y$ $=$ $170$

There were $170$ men who attended the show.
Question 5 of 5

5. Question
Find the value of $x$ and $y$
- $x=$ (5)
  
  $y=$ (3)
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, write the systems of equations being represented in the problem.

$3$ $x$ $-$ $y$ $=$ $12$ Length

$2$ $x$ $+3$ $y$ $=$ $19$ Width

Multiply equation $1$ by $3$

$(3$ $x$ $-$ $y$ $)$ $xx3$ $=$ $12$ $xx3$

$9$ $x$ $-3$ $y$ $=$ $36$

Add the second equation to the transformed equation.

$2$ $x$ $+3$ $y$ $=$ $19$

$9$ $x$ $-3$ $y$ $=$ $36$

$11x$ $=$ $55$

$x$ $=$ $5$ Divide both sides by $11$

Solve for $y$ .

$2$ $x$ $+3$ $y$ $=$ $19$

$2$ $(5)$ $+3$ $y$ $=$ $19$ Substitute $x=5$

$10+3y$ $-10$ $=$ $19$ $-10$ Subtract $10$ from both sides

$3y$ $=$ $9$ Divide both sides by $3$

$y$ $=$ $3$

$x =5$ , $y=3$

$5$ $5$ $a$ $a$ $+ 2$ $+2$ $b$ $b$	$=$ $=$	$2.80$ $2.80$	First occasion
$3$ $3$ $a$ $a$ $+ 5$ $+5$ $b$ $b$	$=$ $=$	$5.10$ $5.10$	Second occasion

$(5$ $(5$ $a$ $a$ $+ 2$ $+2$ $b$ $b$ $)$ $)$ $\times 3$ $xx3$	$=$ $=$	$2.80$ $2.80$ $\times 3$ $xx3$
$15$ $15$ $a$ $a$ $+ 6$ $+6$ $b$ $b$	$=$ $=$	$8.40$ $8.40$

$(3$ $(3$ $a$ $a$ $+ 5$ $+5$ $b$ $b$ $)$ $)$ $\times 5$ $xx5$	$=$ $=$	$5.10$ $5.10$ $\times 5$ $xx5$
$15$ $15$ $a$ $a$ $+ 25$ $+25$ $b$ $b$	$=$ $=$	$25.50$ $25.50$

$15$ $15$ $a$ $a$ $+ 6$ $+6$ $b$ $b$	$=$ $=$	$8.40$ $8.40$
$15$ $15$ $a$ $a$ $+ 25$ $+25$ $b$ $b$	$=$ $=$	$25.50$ $25.50$

$- 19 b$ $-19b$	$=$ $=$	$- 17.10$ $-17.10$
$b$ $b$	$=$ $=$	$0.90$ $0.90$	Divide both sides by $- 19$ $-19$

$3$ $3$ $a$ $a$ $+ 5$ $+5$ $b$ $b$	$=$ $=$	$5.10$ $5.10$
$3$ $3$ $a$ $a$ $+ 5$ $+5$ $(0.90)$ $(0.90)$	$=$ $=$	$5.10$ $5.10$	Substitute $b = 0.90$ $b=0.90$
$3 a + 4.5$ $3a+4.5$ $- 4.5$ $-4.5$	$=$ $=$	$5.10$ $5.10$ $- 4.5$ $-4.5$	Subtract $4.5$ $4.5$ from both sides
$3 a$ $3a$	$=$ $=$	$0.60$ $0.60$	Divide both sides by $3$ $3$
$a$ $a$	$=$ $=$	$0.20$ $0.20$

Systems of Equations Word Problems 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Great Work!

2. Question

Hint

Correct!

3. Question

Hint

Correct!

4. Question

Hint

Keep Going!

5. Question

Hint

Fantastic!

Quizzes

$4$ $4$ $d$ $d$ $+ 3$ $+3$ $p$ $p$	$=$ $=$	$4080$ $4080$	Equation $1$ $1$
$2$ $2$ $d$ $d$ $+ 1$ $+1$ $p$ $p$	$=$ $=$	$1500$ $1500$	Equation $2$ $2$

$2 d + 1 p$ $2d+1p$	$=$ $=$	$1500$ $1500$	Equation $2$ $2$
$(2 d + 1 p)$ $(2d+1p)$ $\times 2$ $times2$	$=$ $=$	$1500$ $1500$ $\times 2$ $times2$	Multiply the values of both sides by $2$ $2$
$4 d + 2 p$ $4d+2p$	$=$ $=$	$3000$ $3000$	Equation $3$ $3$

$4 d - 3 p$ $4d-3p$	$=$	$4080$
$-$ $(4d+2p)$	$=$	$3000$

$p$	$=$	$1080$	$4d-4d$ cancels out

$2d+1$ $p$	$=$	$1500$	Equation $2$
$2d+1$ $(1080)$	$=$	$1500$	$p=1080$
$2d+1080$ $-1080$	$=$	$1500$ $-1080$	Subtract $1080$ from both sides
$2d$ $div2$	$=$	$420$ $div2$	Divide both sides by $2$
$d$	$=$	$210$

$2$ $x$ $+5$ $y$	$=$	$575$	First occasion
$4$ $x$ $+6$ $y$	$=$	$810$	Second occasion

$(2$ $x$ $+5$ $y$ $)$ $xx2$	$=$	$575$ $xx2$
$4$ $x$ $+10$ $y$	$=$	$1150$

$2$ $x$ $+5$ $y$	$=$	$575$
$2$ $x$ $+5$ $(85)$	$=$	$575$	Substitute $y=85$
$2x+425$ $-425$	$=$	$575$ $-425$	Subtract $425$ from both sides
$2x$	$=$	$150$	Divide both sides by $2$
$x$	$=$	$75$

$x$ $+$ $y$	$=$	$400$	There are a total of $400$ patrons
$x$	$=$	$y$ $+60$	$60$ more women than men

$x$	$=$	$y$ $+60$
$x$ $-y$	$=$	$y$ $+60$ $-y$	Subtract $y$ from both sides
$x$ $-$ $y$	$=$	$60$

$x$ $+4$ $y$	$=$	$400$
$x$ $-$ $y$	$=$	$60$

$2x$	$=$	$460$
$x$	$=$	$230$	Divide both sides by $2$

$x$ $-$ $y$	$=$	$60$
$230$ $-$ $y$	$=$	$60$	Substitute $x=230$
$230-y$ $-230$	$=$	$60$ $-230$
$-y$	$=$	$-170$
$y$	$=$	$170$

$3$ $x$ $-$ $y$	$=$	$12$	Length
$2$ $x$ $+3$ $y$	$=$	$19$	Width

$(3$ $x$ $-$ $y$ $)$ $xx3$	$=$	$12$ $xx3$
$9$ $x$ $-3$ $y$	$=$	$36$

$2$ $x$ $+3$ $y$	$=$	$19$
$2$ $(5)$ $+3$ $y$	$=$	$19$	Substitute $x=5$
$10+3y$ $-10$	$=$	$19$ $-10$	Subtract $10$ from both sides
$3y$	$=$	$9$	Divide both sides by $3$
$y$	$=$	$3$