Age Word Problems

Years

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Question 1 of 7

1. Question
Eddie is $4$ years younger than his sister Jessica. The sum of their ages is $28$ 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: $x$

Eddie’s age: $x-4$

Translate the problem into an equation based on the diagram

$x+(x-4)$ $=$ $28$

Solve for $x$

$x+(x-4)$ $=$ $28$

$2x-4$ $=$ $28$

$2x-4$ $+4$ $=$ $28$ $+4$ Add $4$ to both sides

$2x$ $=$ $32$

$2x$ $-:2$ $=$ $32$ $-:2$ Divide both sides by $2$

$x$ $=$ $16$ Jessica’s Age

Solve for $x-4$

$x-4$

$=$ $16-4$ Substitute $x$

$=$ $12$ Eddie’s Age

Jessica’s Age: $16$

Eddie’s Age: $12$

Question 2 of 7

Matt’s age is

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

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

Matt: (33) years old

Eliza: (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 $96$ 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: $x$

Constance’s age: $2x$

Jake’s age: $3x$

Translate the problem into an equation based on the diagram

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

Solve for $x$

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

$6x$ $=$ $96$

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

$x$ $=$ $16$

Solve for $2x$

$2x$

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

$=$ $32$ years old Constance’s Age

$32$ years old

Question 4 of 7

Nicole is

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

$53$ years. In

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

Nicole: (49) years old

Max: (20) years old

Question 5 of 7

When Marvin was

$16$ , 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

Question 6 of 7

Joanna is

$12$ years older than Patrick. But

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

(32) years old

Question 7 of 7

Pete’s Mum is

$42$ years old. In

$9$ years time, she will be

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

$x+(1/7x)$	$=$	$40$

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

	$1/7x$

$=$	$1/7(35)$	Substitute $x$

$=$	$5$	Eliza’s current age

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

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

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

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Quiz summary

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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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Quizzes

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

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

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

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

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

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

		$35-2$
	$=$	$33$

		$41+8$
	$=$	$49$