Equation Word Problems 4

Question 1 of 5

Half of

x

$x$ plus

8

$8$ is equal to half the sum of

3 x

$3x$ and

- 2

$-2$ . Solve for

x

$x$ .

$x =$ $x=$ (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 ( $x, y, z,$ $x,y,z,$ etc)
is the same as, The answer is, is equal	$=$ $=$
sum, and, plus, more than	$+$ $+$
subtracted, less, minus	$-$ $-$
times, product, multiplied, twice	$\times$ $times$
half of, divide by	$\div$ $divide$

First, form an equation using the information given.

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

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

Remove

\frac{1}{2}

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

2

$2$ .

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

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

Move

x

$x$ to the other side by subtracting

x

$x$ from both sides of the equation.

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

Next, move

2

$2$ to the other side by adding

2

$2$ to both sides of the equation.

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

Finally, remove

2

$2$ by dividing both sides of the equation by

2

$2$ .

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

x = 9

$x=9$

Question 2 of 5

5

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

3

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

(5)

Question 3 of 5

The product of a number and

3

$3$ is subtracted from

80

$80$ . If the answer is

38

$38$ , what is the number?

(14)

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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 ( $x, y, z,$ $x,y,z,$ etc)
is the same as, The answer is, is equal	$=$ $=$
sum, and, plus, more than	$+$ $+$
subtracted, less, minus	$-$ $-$
times, product, multiplied, twice	$\times$ $times$
half of, divide by	$\div$ $divide$

First, label the values and form an equation using the information given.

Number

= n

$=n$

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

Simplify the equation:

$80 - (n \times 3)$ $80-(ntimes3)$	$=$ $=$	$38$ $38$
$80 - 3 n$ $80-3n$	$=$ $=$	$38$ $38$

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

Start by moving

80

$80$ to the other side by subtracting

80

$80$ from both sides of the equation.

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

Make both sides of the equation positive by multiplying

- 1

$-1$ to each side.

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

Finally, remove

3

$3$ by dividing both sides of the equation by

3

$3$ .

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

The number is

14

$14$ .

Check our work

To confirm our answer, substitute

n = 14

$n=14$ to the original equation.

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

Since the equation is true, the answer is correct.

14

$14$

Question 4 of 5

What are

3

$3$ consecutive numbers that add up to

72 ?

$72?$

$1$ $1$ st number $=$ $=$ (23)

$2$ $2$ nd number $=$ $=$ (24)

$3$ $3$ rd number $=$ $=$ (25)

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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 ( $x, y, z,$ $x,y,z,$ etc)
is the same as, The answer is, is equal	$=$ $=$
sum, and, plus, more than	$+$ $+$
subtracted, less, minus	$-$ $-$
times, product, multiplied, twice	$\times$ $times$
half of, divide by	$\div$ $divide$

First, label the values and form an equation using the information given.

1

$1$ st number

= x

$=x$

2

$2$ nd number

= x + 1

$=x+1$ (since it comes after the

1

$1$ st number)

3

$3$ rd number

= x + 2

$=x+2$ (since it comes after the

2

$2$ nd number)

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

Simplify the equation:

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

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

Start by moving

3

$3$ to the other side by subtracting

3

$3$ from both sides of the equation.

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

Next, remove

$3$ by dividing both sides of the equation by

$3$ .

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

Substitute $x=23$ to find each number.

$1$ st number	$=$	$x$
	$=$	$23$

$2$ nd number	$=$	$x$ $+1$
	$=$	$23$ $+1$
	$=$	$24$

$3$ rd number	$=$	$x$ $+2$
	$=$	$23$ $+2$
	$=$	$25$

Check our work

To confirm our answer, add the

$3$ numbers and check if the sum is

$72$ .

$23+24+25$	$=$	$72$
$72$	$=$	$72$

Since the equation is true, the answer is correct.

$1$ 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)

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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

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

$2 x + 5$ $2x+5$	$=$ $=$	$3 \times x$ $3timesx$
$2 x + 5$ $2x+5$	$=$ $=$	$3 x$ $3x$

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

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