Age Word Problems
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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 betterJessica’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` -
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Question 2 of 7
2. Question
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 oldEliza: (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 betterMatt’s age: `x`Eliza’s age: `1/7x`
Translate the problem into an equation based on the diagram`x+(1/7x)` `=` `40` Solve for `x``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 Solve for `1/7x``1/7x` `=` `1/7(35)` Substitute `x` `=` `5` Eliza’s current age Finally, solve for their ages `2` years agoMatt:`35-2` `=` `33` Eliza:`5-2` `=` `3` Matt: `33` years oldEliza: `3` years old -
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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 betterBruce’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
4. Question
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 oldMax: (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 betterNicole’s age: `x`Max’s age: `x-29`
Translate the problem into an equation based on the diagram`x``+``x-29` `=` `53` Solve for `x``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 Solve for `x-29``x-29` `=` `41-29` Substitute `x` `=` `12` Max’s current age Finally, solve for their ages in `8` years timeNicole:`41+8` `=` `49` Max:`12+8` `=` `20` Nicole: `49` years oldMax: `20` years old -
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Question 5 of 7
5. Question
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 oldDad: (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 betterMarvin’s current age: `x`Dad’s current age: `2x`Marvin’s age then: `16`Dad’s age then: `3(16)=48`
Translate the problem into an equation based on the diagramNote that the year difference from then and now is equal for both Marvin and his dad`16-x` `=` `48-2x` Solve for `x``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 Solve for `2x``2x` `=` `2(32)` Substitute `x` `=` `64` Dad’s age now Marvin: `32` years oldDad: `64` years old -
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Question 6 of 7
6. Question
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
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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 betterPatrick’s age: `x`Joanna’s age: `x+12`Patrick’s age `20` years ago: `x-20`Joanna’s age `20` years ago: `(x+12)-20=x-8`
Translate the problem into an equation based on the diagram`20` years ago, twice Patrick’s age is Joanna’s age `2(x-20)` `=` `x-8` Solve for `x``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 `32` years old -
Question 7 of 7
7. Question
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?- (8)
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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 betterPete’s age: `x`Mum’s age: `42`Pete’s age after `9` years: `x+9`Mum’s age after `9` years: `42+9`
Note that from here, we know that the age of Pete’s Mum in `9` years is `51`Translate the problem into an equation based on the diagramIn `9` years, `3` times Peter’s age is his Mum’s age `3(x+9)` `=` `51` Solve for `x``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 `8`