Age Word Problems

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Question 1 of 7

Eddie is

4

$4$ years younger than his sister Jessica. The sum of their ages is

28

$28$ years. Find their ages.

Jessica's Age: (16)

Eddie's Age: (12)

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Jessica’s age:

x

$x$

Eddie’s age:

x - 4

$x-4$

Translate the problem into an equation based on the diagram

x + (x - 4)

$x+(x-4)$

=

$=$

28

$28$

Solve for

x

$x$

$x + (x - 4)$ $x+(x-4)$	$=$ $=$	$28$ $28$
$2 x - 4$ $2x-4$	$=$ $=$	$28$ $28$
$2 x - 4$ $2x-4$ $+ 4$ $+4$	$=$ $=$	$28$ $28$ $+ 4$ $+4$	Add $4$ $4$ to both sides
$2 x$ $2x$	$=$ $=$	$32$ $32$
$2 x$ $2x$ $\div 2$ $-:2$	$=$ $=$	$32$ $32$ $\div 2$ $-:2$	Divide both sides by $2$ $2$
$x$ $x$	$=$ $=$	$16$ $16$	Jessica’s Age

Solve for

x - 4

$x-4$

	$x - 4$ $x-4$
$=$ $=$	$16 - 4$ $16-4$	Substitute $x$ $x$
$=$ $=$	$12$ $12$	Eddie’s Age

Jessica’s Age:

16

$16$

Eddie’s Age:

12

$12$

Question 2 of 7

Matt’s age is

7

$7$ times that of Eliza’s age. Their combined ages is

40

$40$ years. How old were they two years ago?

Matt: (33) years old

Eliza: (3) years old

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Matt’s age:

x

$x$

Eliza’s age:

\frac{1}{7} x

$1/7x$

Translate the problem into an equation based on the diagram

x + (\frac{1}{7} x)

$x+(1/7x)$

=

$=$

40

$40$

Solve for

x

$x$

$x + (\frac{1}{7} x)$ $x+(1/7x)$	$=$ $=$	$40$ $40$

$x + (\frac{1}{7} x)$ $x+(1/7x)$ $\times 7$ $times7$	$=$ $=$	$40$ $40$ $\times 7$ $times7$	Multiply $7$ $7$ to both sides
$7 x + x$ $7x+x$	$=$ $=$	$280$ $280$
$8 x$ $8x$	$=$ $=$	$280$ $280$
$8 x$ $8x$ $\div 8$ $-:8$	$=$ $=$	$280$ $280$ $\div 8$ $-:8$	Divide both sides by $8$ $8$
$x$ $x$	$=$ $=$	$35$ $35$	Matt’s current age

Solve for

\frac{1}{7} x

$1/7x$

	$\frac{1}{7} x$ $1/7x$

$=$ $=$	$\frac{1}{7} (35)$ $1/7(35)$	Substitute $x$ $x$

$=$ $=$	$5$ $5$	Eliza’s current age

Finally, solve for their ages

2

$2$ years ago

Matt:

		$35 - 2$ $35-2$
	$=$ $=$	$33$ $33$

Eliza:

		$5 - 2$ $5-2$
	$=$ $=$	$3$ $3$

Matt:

33

$33$ years old

Eliza:

3

$3$ years old

Question 3 of 7

3. Question
Jake is three times as old as Bruce. Bruce is half as old as Constance. The combined ages of the three is $96$ $96$ years. How old is Constance?
- (32) years old
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Bruce’s age: $x$ $x$

Constance’s age: $2 x$ $2x$

Jake’s age: $3 x$ $3x$

Translate the problem into an equation based on the diagram

$x + 2 x + 3 x$ $x+2x+3x$ $=$ $=$ $96$ $96$

Solve for $x$ $x$

$x + 2 x + 3 x$ $x+2x+3x$ $=$ $=$ $96$ $96$

$6 x$ $6x$ $=$ $=$ $96$ $96$

$6 x$ $6x$ $\div 6$ $-:6$ $=$ $=$ $96$ $96$ $\div 6$ $-:6$ Divide both sides by $6$ $6$

$x$ $x$ $=$ $=$ $16$ $16$

Solve for $2 x$ $2x$

$2 x$ $2x$

$=$ $=$ $2 (16)$ $2(16)$ Substitute $x$ $x$

$=$ $=$ $32$ $32$ years old Constance’s Age

$32$ $32$ years old

Question 4 of 7

Nicole is

29

$29$ years older than her son Max. The sum of their ages is

53

$53$ years. In

8

$8$ years time, what will their ages be?

Nicole: (49) years old

Max: (20) years old

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Nicole’s age:

x

$x$

Max’s age:

x - 29

$x-29$

Translate the problem into an equation based on the diagram

$x$ $x$

+

$+$ $x - 29$ $x-29$

=

$=$

53

$53$

Solve for

x

$x$

$x$ $x$ $+$ $+$ $x - 29$ $x-29$	$=$ $=$	$53$ $53$
$2 x - 29$ $2x-29$	$=$ $=$	$53$ $53$	$x + x = 2 x$ $x+x=2x$
$2 x - 29$ $2x-29$ $+ 29$ $+29$	$=$ $=$	$53$ $53$ $+ 29$ $+29$	Add $29$ $29$ to both sides
$2 x$ $2x$	$=$ $=$	$82$ $82$
$2 x$ $2x$ $\div 2$ $-:2$	$=$ $=$	$82$ $82$ $\div 2$ $-:2$	Divide both sides by $2$ $2$
$x$ $x$	$=$ $=$	$41$ $41$	Nicole’s current age

Solve for

x - 29

$x-29$

	$x - 29$ $x-29$
$=$ $=$	$41 - 29$ $41-29$	Substitute $x$ $x$
$=$ $=$	$12$ $12$	Max’s current age

Finally, solve for their ages in

8

$8$ years time

Nicole:

		$41 + 8$ $41+8$
	$=$ $=$	$49$ $49$

Max:

		$12 + 8$ $12+8$
	$=$ $=$	$20$ $20$

Nicole:

49

$49$ years old

Max:

20

$20$ years old

Question 5 of 7

When Marvin was

16

$16$ , his father was three times his age. Now, his father is only twice Marvin’s age. How old are they now?

Marvin: (32) years old

Dad: (64) years old

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Marvin’s current age:

x

$x$

Dad’s current age:

2 x

$2x$

Marvin’s age then:

16

$16$

Dad’s age then:

3 (16) = 48

$3(16)=48$

Translate the problem into an equation based on the diagram

Note that the year difference from then and now is equal for both Marvin and his dad

16 - x

$16-x$

=

$=$

48 - 2 x

$48-2x$

Solve for

x

$x$

$16 - x$ $16-x$	$=$ $=$	$48 - 2 x$ $48-2x$
$16 - x$ $16-x$ $+ 2 x$ $+2x$	$=$ $=$	$48 - 2 x$ $48-2x$ $+ 2 x$ $+2x$	Add $2 x$ $2x$ to both sides
$16 + x$ $16+x$	$=$ $=$	$48$ $48$
$16 + x$ $16+x$ $- 16$ $-16$	$=$ $=$	$48$ $48$ $- 16$ $-16$	Subtract $16$ $16$ from both sides
$x$ $x$	$=$ $=$	$32$ $32$	Marvin’s age now

Solve for

2 x

$2x$

	$2 x$ $2x$
$=$ $=$	$2 (32)$ $2(32)$	Substitute $x$ $x$

$=$ $=$	$64$ $64$	Dad’s age now

Marvin:

32

$32$ years old

Dad:

64

$64$ years old

Question 6 of 7

Joanna is

12

$12$ years older than Patrick. But

20

$20$ years ago, Joanna was twice Patrick’s age. Find Patrick’s current age.

(32) years old

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Patrick’s age:

x

$x$

Joanna’s age:

x + 12

$x+12$

Patrick’s age

20

$20$ years ago:

x - 20

$x-20$

Joanna’s age

20

$20$ years ago:

(x + 12) - 20 = x - 8

$(x+12)-20=x-8$

Translate the problem into an equation based on the diagram

$20$ $20$ years ago, twice Patrick’s age	is	Joanna’s age
$2 (x - 20)$ $2(x-20)$	$=$ $=$	$x - 8$ $x-8$

Solve for

x

$x$

$2 (x - 20)$ $2(x-20)$	$=$ $=$	$x - 8$ $x-8$
$2 x - 40$ $2x-40$	$=$ $=$	$x - 8$ $x-8$
$2 x - 40$ $2x-40$ $- x$ $-x$	$=$ $=$	$x - 8$ $x-8$ $- x$ $-x$	Subtract $x$ $x$ from both sides
$x - 40$ $x-40$	$=$ $=$	$- 8$ $-8$
$x - 40$ $x-40$ $+ 40$ $+40$	$=$ $=$	$- 8$ $-8$ $+ 40$ $+40$	Add $40$ $40$ to both sides
$x$ $x$	$=$ $=$	$32$ $32$ years old	Patrick’s current age

32

$32$ years old

Question 7 of 7

Pete’s Mum is

42

$42$ years old. In

9

$9$ years time, she will be

3

$3$ times as old as Pete. How old is Pete now?

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A word problem can be drawn as a diagram and then translated into an equation for easier solving.

First, draw a diagram of the problem in order to understand it better

Pete’s age:

x

$x$

Mum’s age:

42

$42$

Pete’s age after

9

$9$ years:

x + 9

$x+9$

Mum’s age after

9

$9$ years:

42 + 9

$42+9$

Note that from here, we know that the age of Pete’s Mum in

9

$9$ years is

51

$51$

Translate the problem into an equation based on the diagram

In $9$ $9$ years, $3$ $3$ times Peter’s age	is	his Mum’s age
$3 (x + 9)$ $3(x+9)$	$=$ $=$	$51$ $51$

Solve for

x

$x$

$3 (x + 9)$ $3(x+9)$	$=$ $=$	$51$ $51$
$3 x + 27$ $3x+27$	$=$ $=$	$51$ $51$
$3 x + 27$ $3x+27$ $- 27$ $-27$	$=$ $=$	$51$ $51$ $- 27$ $-27$	Subtract $27$ $27$ from both sides
$3 x$ $3x$	$=$ $=$	$24$ $24$
$3 x$ $3x$ $\div 3$ $-:3$	$=$ $=$	$24$ $24$ $\div 3$ $-:3$	Divide both sides by $3$ $3$
$x$ $x$	$=$ $=$	$8$ $8$	Pete’s current age

8

$8$

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Quiz summary

Information

1. Question

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Fantastic!

2. Question

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Excellent!

3. Question

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Nice Job!

4. Question

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Well Done!

5. Question

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Great Work!

6. Question

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Correct!

7. Question

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Keep Going!

Quizzes

$x + 2 x + 3 x$ $x+2x+3x$	$=$ $=$	$96$ $96$
$6 x$ $6x$	$=$ $=$	$96$ $96$
$6 x$ $6x$ $\div 6$ $-:6$	$=$ $=$	$96$ $96$ $\div 6$ $-:6$	Divide both sides by $6$ $6$
$x$ $x$	$=$ $=$	$16$ $16$

	$2 x$ $2x$
$=$ $=$	$2 (16)$ $2(16)$	Substitute $x$ $x$
$=$ $=$	$32$ $32$ years old	Constance’s Age