Equation Word Problems (Age)

Years

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Question 1 of 5

Luke is

$5$ years younger than his brother James. The sum of their ages is

$35$ . How old is Luke?

(15) years old

Question 2 of 5

Sophia is

$4$ years younger than her sister Irene. The sum of their ages is

$32$ years. How old are they?

Sophia is (14) years old

Irene is (18) years old

Question 3 of 5

When Grace was

$6$ years old, her mother was

$25$ years old. Now, Grace’s mother is twice as old as Grace. How old is Grace now?

(19) years old

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Inverse Operations

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

Distributive Property

$a$

$(b+c)=$ $a$

$b+$ $a$

$c$

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, find the difference between Grace’s age and her mother’s based on the given information.

Grace’s age

$=6$

Her mother’s age

$=25$

Her Mother’s Age $-$ Grace’s Age	$=$	$25-6$
	$=$	$19$

Use the information gathered so far to label the values and form an equation.

Her mother’s age

$=x$

Grace’s age

$=x-19$ (since she is

$19$ years younger)

Grace’s mother	is	twice as old as	Grace
$x$	$=$	$2times$	$x-19$

Simplify the equation:

$x$	$=$	$2times(x-19)$
$x$	$=$	$2(x-19)$

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

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

$x$	$=$	$2$ $($ $x$ $-19)$
$x$	$=$	$2$ $x$ $-$ $2$ $(19)$
$x$	$=$	$2$ $x$ $-38$

Next, move

$2x$ to the other side by subtracting

$2x$ from both sides of the equation.

$x$	$=$	$2$ $x$ $-38$
$x$ $-2x$	$=$	$2$ $x$ $-38$ $-2x$
$-$ $x$	$=$	$-38$	$2x-2x$ cancels out

Make both sides positive by multiplying

$-1$ .

$-$ $x$	$=$	$-38$
$-$ $x$ $times-1$	$=$	$-38$ $times-1$
$x$	$=$	$38$

Substitute $x=38$ to get the age of Grace and her mother.

Her mother’s age	$=$	$x$
	$=$	$38$ years old

Grace’s age	$=$	$x$ $-19$
	$=$	$38$ $-19$
	$=$	$19$ years old

$19$ years old

Question 4 of 5

When Jack was born, his father was

$28$ years old. His father is now

$3$ times as old as Jack. What are their ages now?

Jack is (14) years old

His father is (42) years old

Question 5 of 5

Alan’s age is

$6$ times that of Noah’s. Their combined ages is

$42$ years. Three years ago, how old were they?

Noah was (3) years old

Alan was (33) years old

Luke’s age	$=$	$x$ $-5$
	$=$	$20$ $-5$	Substitute $x=20$
	$=$	$15$

Irene’s age	$=$	$x$ $+4$
	$=$	$14$ $+4$
	$=$	$18$ years old

$x+28$	$=$	$3timesx$
$x+28$	$=$	$3x$

His father’s age	$=$	$x$ $+28$
	$=$	$14$ $+28$
	$=$	$42$ years old

Noah’s age $3$ years ago	$=$	$6$ $-3$
	$=$	$3$ years old

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Quiz summary

Information

1. Question

Hint

Well Done!

Inverse Operations

2. Question

Hint

Good Job!

Inverse Operations

3. Question

Hint

Fantastic!

Inverse Operations

Distributive Property

4. Question

Hint

Well Done!

Inverse Operations

5. Question

Hint

Great Work!

Inverse Operations

Quizzes

$2$ $x$ $-5$	$=$	$35$
$2$ $x$ $-5$ $+5$	$=$	$35$ $+5$
$2$ $x$	$=$	$40$	$-5+5$ cancels out

$2$ $x$	$=$	$40$
$2$ $x$ $divide2$	$=$	$40$ $divide2$
$x$	$=$	$20$	$2divide2$ cancels out

Sophia’s age	and	Irene’s age	add up to	$32$
$x$	$+$	$x+4$	$=$	$32$

$2$ $x$ $+4$	$=$	$32$
$2$ $x$ $+4$ $-4$	$=$	$32$ $-4$
$2$ $x$	$=$	$28$	$4-4$ cancels out

$x$ $+28$	$=$	$3$ $x$
$x$ $+28$ $-x$	$=$	$3$ $x$ $-x$
$28$	$=$	$2$ $x$	$x-x$ cancels out

$28$	$=$	$2$ $x$
$28$ $divide2$	$=$	$2$ $x$ $divide2$
$14$	$=$	$x$	$2divide2$ cancels out
$x$	$=$	$14$

$7$ $x$	$=$	$42$
$7$ $x$ $divide7$	$=$	$42$ $divide7$
$x$	$=$	$6$	$7divide7$ cancels out