Equation Word Problems (Age) 1

Question 1 of 5

Luke is

5

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

35

$35$ . How old is Luke?

(15) years old

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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.

James’ age

= x

$=x$

Luke’s age

= x - 5

$=x-5$ (since he is

5

$5$ years younger)

James’ age	and	Luke’s age	add up to	$35$ $35$
$x$ $x$	$+$ $+$	$x - 5$ $x-5$	$=$ $=$	$35$ $35$

Simplify the equation:

$x + x - 5$ $x+x-5$	$=$ $=$	$35$ $35$
$2 x - 5$ $2x-5$	$=$ $=$	$35$ $35$

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

Start by moving

- 5

$-5$ to the other side by adding

5

$5$ to both sides of the equation.

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

Next, remove

2

$2$ by dividing both sides of the equation by

2

$2$ .

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

James is

20

$20$ years old.

Now that we know James’ age, we can compute for Luke’s as well.

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

Luke is

15

$15$ years old.

15

$15$ years old

Question 2 of 5

Sophia is

4

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

32

$32$ years. How old are they?

Sophia is (14) years old

Irene is (18) years old

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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.

Sophia’s age

= x

$=x$

Irene’s age

= x + 4

$=x+4$ (since she is

4

$4$ years older)

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

Simplify the equation:

$x + x + 4$ $x+x+4$	$=$ $=$	$32$ $32$
$2 x + 4$ $2x+4$	$=$ $=$	$32$ $32$

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

Start by moving

4

$4$ to the other side by subtracting

4

$4$ from both sides of the equation.

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

Next, remove

2

$2$ by dividing both sides of the equation by

2

$2$ .

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

Substitute $x = 14$ $x=14$ to get the age of Sophia and Irene.

Sophia’s age	$=$ $=$	$x$ $x$
	$=$ $=$	$14$ $14$ years old

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

Sophia is

14

$14$ years old

Irene is

18

$18$ years old

Question 3 of 5

When Grace was

6

$6$ years old, her mother was

25

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

(19) years old

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Grace’s age

= 6

$=6$

Her mother’s age

= 25

$=25$

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

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

Her mother’s age

= x

$=x$

Grace’s age

= x - 19

$=x-19$ (since she is

19

$19$ years younger)

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

Simplify the equation:

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

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

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

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

Next, move

2 x

$2x$ to the other side by subtracting

2 x

$2x$ from both sides of the equation.

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

Make both sides positive by multiplying

- 1

$-1$ .

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

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

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

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

19

$19$ years old

Question 4 of 5

When Jack was born, his father was

28

$28$ years old. His father is now

3

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

Jack is (14) years old

His father is (42) years old

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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	$\div$ $divide$

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

Jack’s age

= x

$=x$

His father’s age

= x + 28

$=x+28$ (since he was

28

$28$ years old when Jack was born)

His father	is	$3$ $3$ times as old as	Jack
$x + 28$ $x+28$	$=$ $=$	$3 \times$ $3times$	$x$ $x$

Simplify the equation:

$x + 28$ $x+28$	$=$ $=$	$3 \times x$ $3timesx$
$x + 28$ $x+28$	$=$ $=$	$3 x$ $3x$

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

Start by moving

x

$x$ to the other side by subtracting

x

$x$ from both sides of the equation.

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

Next, remove

2

$2$ by dividing both sides of the equation by

2

$2$ .

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

Substitute $x = 14$ $x=14$ to get the age of Jack and his father.

Jack’s age	$=$ $=$	$x$ $x$
	$=$ $=$	$14$ $14$ years old

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

Jack is

14

$14$ years old

His father is

42

$42$ years old

Question 5 of 5

Alan’s age is

6

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

42

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

Noah was (3) years old

Alan was (33) years old

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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	$\div$ $divide$

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

Noah’s age

= x

$=x$

Alan’s age

= 6 x

$=6x$ (since he

6

$6$ times as old as Noah)

Alan and Noah’s combined ages	is	$42$ $42$
$x + 6 x$ $x+6x$	$=$ $=$	$42$ $42$

Simplify the equation:

$x + 6 x$ $x+6x$	$=$ $=$	$42$ $42$
$7 x$ $7x$	$=$ $=$	$42$ $42$

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

Remove

7

$7$ by dividing both sides of the equation by

7

$7$ .

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

Substitute $x = 6$ $x=6$ to get Noah and Alan’s age now.

Noah’s age	$=$ $=$	$x$ $x$
	$=$ $=$	$6$ $6$ years old

Alan’s age	$=$ $=$	$6$ $6$ $x$ $x$
	$=$ $=$	$6 ($ $6($ $6$ $6$ $)$ $)$
	$=$ $=$	$36$ $36$ years old

Finally, subtract

3

$3$ from each of their current ages to get Noah and Alan’s age three years ago.

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

Alan’s age $3$ $3$ years ago	$=$ $=$	$36$ $36$ $- 3$ $-3$
	$=$ $=$	$33$ $33$ years old

Noah was

3

$3$ years old

Alan was

33

$33$ years old

Equation Word Problems (Age) 1

Try VividMath Premium to unlock full access

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