Simultaneous Equations Word Problems 1

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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

$2$ oranges and

5

$5$ apples cost

$ 5.75

$$5.75$ and

4

$4$ oranges and

6

$6$ apples cost

$ 8.10

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

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

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

Question 4 of 5

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

$x =$ $x=$ number of women

$y =$ $y=$ number of men

Next, write the simultaneous equations being represented in the problem.

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

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

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

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

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

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

Add the two equations.

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

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

$2 x$ $2x$ $=$ $=$ $460$ $460$

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

Solve for $y$ $y$ , the number of men.

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

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

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

$- y$ $-y$ $=$ $=$ $- 170$ $-170$

$y$ $y$ $=$ $=$ $170$ $170$

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

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

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

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

Multiply equation $1$ $1$ by $3$ $3$

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

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

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 $3$ $3$
$a$ $a$	$=$ $=$	$0.20$ $0.20$

Simultaneous Equations Word Problems 1

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Quiz summary

Information

1. Question

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Great Work!

2. Question

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Correct!

3. Question

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Correct!

4. Question

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Keep Going!

5. Question

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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 $3$ $3$

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

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

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

$d$ $d$	$=$ $=$	$210 \div 100$ $210div100$
	$=$ $=$	$$ 2.10$ $$2.10$

$p$ $p$	$=$ $=$	$1080 \div 100$ $1080div100$
	$=$ $=$	$$ 10.80$ $$10.80$

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

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

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

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

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

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

$2$ $x$ $+3$ $y$	$=$	$19$
$9$ $x$ $-3$ $y$	$=$	$36$

$11x$	$=$	$55$
$x$	$=$	$5$	Divide both sides by $11$

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

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