Equation Word Problems 4

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Year 8

Equations

Equation Word Problems

Equation Word Problems 4

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Question 1 of 5

Half of

$x$ plus

$8$ is equal to half the sum of

$3x$ and

$-2$ . Solve for

$x$ .

$x=$ (9)

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Inverse Operations

When moving a term to the other side of an equation, the operation is inversed.

Keywords for Word Problems
Keyword	Meaning
Certain number	Unknown variable ( $x,y,z,$ etc)
is the same as, The answer is, is equal	$=$
sum, and, plus, more than	$+$
subtracted, less, minus	$-$
times, product, multiplied, twice	$times$
half of, divide by	$divide$

First, form an equation using the information given.

Half of $x$	plus	$8$	is equal to	half	the sum of $3x$ and $-2$
$x/2$	$+$	$8$	$=$	$1/2$	$(3x-2)$

To solve for $x$ , it needs to be alone on one side.

Remove

$1/2$ by multiplying both sides of the equation by

$2$ .

$\frac{\color{#00880A}{x}}{2}+8$	$=$	$1/2(3$ $x$ $-2)$

$\left(\frac{\color{#00880A}{x}}{2}+8\right)\color{#CC0000}{\times2}$	$=$	$1/2(3$ $x$ $-2)$ $times2$
$x$ $+16$	$=$	$3$ $x$ $-2$	$1/2times2$ cancels out

Move

$x$ to the other side by subtracting

$x$ from both sides of the equation.

$x$ $+16$	$=$	$3$ $x$ $-2$
$x$ $+16$ $-x$	$=$	$3$ $x$ $-2$ $-x$
$16$	$=$	$2$ $x$ $-2$	$x-x$ cancels out

Next, move

$2$ to the other side by adding

$2$ to both sides of the equation.

$16$	$=$	$2$ $x$ $-2$
$16$ $+2$	$=$	$2$ $x$ $-2$ $+2$
$18$	$=$	$2$ $x$	$-2+2$ cancels out

Finally, remove

$2$ by dividing both sides of the equation by

$2$ .

$18$	$=$	$2$ $x$
$18$ $divide2$	$=$	$2$ $x$ $divide2$
$9$	$=$	$x$	$2divide2$ cancels out
$x$	$=$	$9$

$x=9$

Question 2 of 5

$5$ more than twice a number is the same as

$3$ times that number. What is the number?

Question 3 of 5

The product of a number and

$3$ is subtracted from

$80$ . If the answer is

$38$ , what is the number?

(14)

Question 4 of 5

What are

$3$ consecutive numbers that add up to

$72?$

$1$ st number $=$ (23)

$2$ nd number $=$ (24)

$3$ rd number $=$ (25)

Question 5 of 5

The sum of three consecutive odd numbers is

$51$ . Find the numbers.

$1$ st number $=$ (15)

$2$ nd number $=$ (17)

$3$ rd number $=$ (19)

$80-3$ $n$	$=$	$38$
$80-3$ $n$ $-80$	$=$	$38$ $-80$
$-3$ $n$	$=$	$-42$	$80-80$ cancels out

$-3$ $n$	$=$	$-42$
$-3$ $n$ $times-1$	$=$	$-42$ $times-1$
$3$ $n$	$=$	$42$

$3$ $n$	$=$	$42$
$3$ $n$ $divide3$	$=$	$42$ $divide3$
$n$	$=$	$14$	$3divide3$ cancels out

The sum of three consecutive numbers	is	$72$
$x+x+1+x+2$	$=$	$72$

$x+x+1+x+2$	$=$	$72$
$3x+3$	$=$	$72$

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Quiz summary

Information

1. Question

Hint

Excellent!

Inverse Operations

2. Question

Hint

Well Done!

Inverse Operations

3. Question

Hint

Excellent!

Inverse Operations

4. Question

Hint

Excellent!

Inverse Operations

5. Question

Hint

Exceptional!

Inverse Operations

Quizzes

$5$ more than twice a number	is the same as	$3$	times	that number
$2x+5$	$=$	$3$	$times$	$x$

$2$ $x$ $+5$	$=$	$3$ $x$
$2$ $x$ $+5$ $-2x$	$=$	$3$ $x$ $-2x$
$5$	$=$	$x$	$2x-2x$ cancels out
$x$	$=$	$5$

The product of a number and $3$ is subtracted from $80$ .	The answer is	$38$
$80-(ntimes3)$	$=$	$38$

$80-3n$	$=$	$38$
$80-3(14)$	$=$	$38$	Substitute $n=14$
$80-42$	$=$	$38$
$38$	$=$	$38$

$3$ $x$ $+3$	$=$	$72$
$3$ $x$ $+3$ $-3$	$=$	$72$ $-3$
$3$ $x$	$=$	$69$	$3-3$ cancels out

$3$ $x$	$=$	$69$
$3$ $x$ $divide3$	$=$	$69$ $divide3$
$x$	$=$	$23$	$3divide3$ cancels out

The sum of three consecutive odd numbers	is	$51$
$x+x+2+x+4$	$=$	$51$

$3$ $x$ $+6$	$=$	$51$
$3$ $x$ $+6$ $-6$	$=$	$51$ $-6$
$3$ $x$	$=$	$45$	$6-6$ cancels out