Equation Word Problems 3

Question 1 of 4

If the sum of a number and

5

$5$ is multiplied by

3

$3$ , the answer is the same as twice the number plus

26

$26$ . What is the number?

(11)

Incorrect

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Inverse Operations

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

Distributive Property

$a$ $a$

(b + c) =

$(b+c)=$ $a$ $a$

b +

$b+$ $a$ $a$

c

$c$

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

$=n$

If the sum of a number and $5$ $5$	is multiplied by	$3$ $3$ ,	the answer is the same as	twice	the number	plus	$26$ $26$
$n + 5$ $n+5$	$\times$ $times$	$3$ $3$	$=$ $=$	$2 \times$ $2times$	$n$ $n$	$+$ $+$	$26$ $26$

Simplify the equation:

$(n + 5) \times 3$ $(n+5)times3$	$=$ $=$	$(2 \times n) + 26$ $(2timesn)+26$
$3 (n + 5)$ $3(n+5)$	$=$ $=$	$2 n + 26$ $2n+26$

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

Start by expanding the left side of the equation by using the Distributive Property.

$3$ $3$ $($ $($ $n$ $n$ $+ 5)$ $+5)$	$=$ $=$	$2$ $2$ $n$ $n$ $+ 26$ $+26$
$3$ $3$ $n$ $n$ $+$ $+$ $3$ $3$ $(5)$ $(5)$	$=$ $=$	$2$ $2$ $n$ $n$ $+ 26$ $+26$
$3$ $3$ $n$ $n$ $+ 15$ $+15$	$=$ $=$	$2$ $2$ $n$ $n$ $+ 26$ $+26$

Next, move

2 n

$2n$ to the other side by subtracting

2 n

$2n$ from both sides of the equation.

$3$ $3$ $n$ $n$ $+ 15$ $+15$	$=$ $=$	$2$ $2$ $n$ $n$ $+ 26$ $+26$
$3$ $3$ $n$ $n$ $+ 15$ $+15$ $- 2 n$ $-2n$	$=$ $=$	$2$ $2$ $n$ $n$ $+ 26$ $+26$ $- 2 n$ $-2n$
$n$ $n$ $+ 15$ $+15$	$=$ $=$	$26$ $26$	$2 n - 2 n$ $2n-2n$ cancels out

Finally, move

15

$15$ to the other side by subtracting

15

$15$ from both sides of the equation.

$n$ $n$ $+ 15$ $+15$	$=$ $=$	$26$ $26$
$n$ $n$ $+ 15$ $+15$ $- 15$ $-15$	$=$ $=$	$26$ $26$ $- 15$ $-15$
$n$ $n$	$=$ $=$	$11$ $11$	$15 - 15$ $15-15$ cancels out

The number is

11

$11$ .

Check our work

To confirm our answer, substitute

n = 11

$n=11$ to the original equation.

$3 (n + 5)$ $3(n+5)$	$=$ $=$	$2 n + 26$ $2n+26$
$3 (11 + 5)$ $3(11+5)$	$=$ $=$	$2 (11) + 26$ $2(11)+26$	Substitute $n = 11$ $n=11$
$3 (16)$ $3(16)$	$=$ $=$	$22 + 26$ $22+26$
$48$ $48$	$=$ $=$	$48$ $48$

Since the equation is true, the answer is correct.

11

$11$

Question 2 of 4

A number is divided by

5

$5$ plus

3

$3$ equals twice the number and

12

$12$ . What is the number?

(-5)

Incorrect

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Inverse Operations

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

Distributive Property

$a$ $a$

$(b+c)=$ $a$

$b+$ $a$

$c$

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

Number

$=n$

A number	is divided by	$5$	plus	$3$	equals	twice	the number	and	$12$
$n$	$divide$	$5$	$+$	$3$	$=$	$2times$	$n$	$+$	$12$

Simplify the equation:

$(ndivide5)+3$	$=$	$(2timesn)+12$

$n/5 +3$	$=$	$2n+12$

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

Start by removing

$1/5$ by multiplying both sides of the equation by

$5$ .

$\frac{\color{#00880A}{n}}{5}+3$	$=$	$2$ $n$ $+12$

$\left(\frac{\color{#00880A}{n}}{5}+3\right)\color{#CC0000}{\times5}$	$=$	$(2$ $n$ $+12)$ $times5$

$n$ $+15$	$=$	$5(2$ $n$ $+12)$	$1/5times5$ cancels out

Next, expand the right side of the equation using the Distributive Property.

$n$ $+15$	$=$	$5$ $(2$ $n$ $+12)$
$n$ $+15$	$=$	$5$ $(2$ $n$ $)+$ $5$ $(12)$
$n$ $+15$	$=$	$10$ $n$ $+60$

Now, move

$n$ to the other side by subtracting

$n$ from both sides of the equation.

$n$ $+15$	$=$	$10$ $n$ $+60$
$n$ $+15$ $-n$	$=$	$10$ $n$ $+60$ $-n$
$15$	$=$	$9$ $n$ $+60$	$n-n$ cancels out

Then, move

$60$ to the other side by subtracting

$60$ from both sides of the equation.

$15$	$=$	$9$ $n$ $+60$
$15$ $-60$	$=$	$9$ $n$ $+60$ $-60$
$-45$	$=$	$9$ $n$	$60-60$ cancels out

Finally, remove

$9$ by dividing both sides of the equation by

$9$ .

$-45$	$=$	$9$ $n$
$-45$ $divide9$	$=$	$9$ $n$ $divide9$
$-5$	$=$	$n$	$9divide9$ cancels out
$n$	$=$	$-5$

The number is

$-5$ .

Check our work

To confirm our answer, substitute

$n=-5$ to the original equation.

$n/5 +3$	$=$	$2n+12$

$(-5)/5 +3$	$=$	$2(-5)+12$	Substitute $n=-5$

$-1+3$	$=$	$-10+12$
$2$	$=$	$2$

Since the equation is true, the answer is correct.

$-5$

Question 3 of 4

The sum of a number and

$3$ is multiplied by

$5$ . The answer is the same as

$3$ times the number plus

$21$ . What is the number?

(3)

Question 4 of 4

The sum of

$3$ consecutive numbers is

$36$ . What are the numbers?

$1$ st number $=$ (11)

$2$ nd number $=$ (12)

$3$ rd number $=$ (13)

$(x+3)times5$	$=$	$(3timesx)+21$
$5(x+3)$	$=$	$3x+21$

$5$ $($ $x$ $+3)$	$=$	$3$ $x$ $+21$
$5$ $x$ $+$ $5$ $(3)$	$=$	$3$ $x$ $+21$
$5$ $x$ $+15$	$=$	$3$ $x$ $+21$

$5$ $x$ $+15$	$=$	$3$ $x$ $+21$
$5$ $x$ $+15$ $-3x$	$=$	$3$ $x$ $+21$ $-3x$
$2$ $x$ $+15$	$=$	$21$	$3x-3x$ cancels out

$2$ $x$	$=$	$6$
$2$ $x$ $divide2$	$=$	$6$ $divide2$
$x$	$=$	$3$	$2divide2$ cancels out

$3$ $x$ $+3$	$=$	$36$
$3$ $x$ $+3$ $-3$	$=$	$36$ $-3$
$3$ $x$	$=$	$33$	$3-3$ cancels out

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Quiz summary

Information

1. Question

Hint

Well Done!

Inverse Operations

Distributive Property

2. Question

Hint

Great Work!

Inverse Operations

Distributive Property

3. Question

Hint

Good Job!

Inverse Operations

Distributive Property

4. Question

Hint

Fantastic!

Inverse Operations

Quizzes

The sum of a number and $3$	is multiplied by	$5$ .	The answer is the same as	$3$	times	the number	plus	$21$
$x+3$	$times$	$5$	$=$	$3$	$times$	$x$	$+$	$21$

$2$ $x$ $+15$	$=$	$21$
$2$ $x$ $+15$ $-15$	$=$	$21$ $-15$
$2$ $x$	$=$	$6$	$15-15$ cancels out

The sum of three consecutive numbers	is	$36$
$x+x+1+x+2$	$=$	$36$

$3$ $x$	$=$	$33$
$3$ $x$ $divide3$	$=$	$33$ $divide3$
$x$	$=$	$11$	$3divide3$ cancels out