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Equation Word Problems (Age)
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Question 1 of 5
1. Question
Luke is `5` years younger than his brother, James. The sum of their ages is `35`. How old is Luke?- (15) years old
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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,` 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, label the values and form an equation using the information given.James’ age`=x`Luke’s age`=x-5` (since he is `5` years younger)James’ age and Luke’s age add up to `35` `x` `+` `x-5` `=` `35` Simplify the equation:`x+x-5` `=` `35` `2x-5` `=` `35` To solve for `x`, it needs to be alone on one side.Start by moving `-5` to the other side by adding `5` to both sides of the equation.`2``x` `-5` `=` `35` `2``x` `-5` `+5` `=` `35` `+5` `2``x` `=` `40` `-5+5` cancels out Next, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `40` `2``x``divide2` `=` `40``divide2` `x` `=` `20` `2divide2` cancels out James is `20` years old.Now that we know James’ age, we can compute for Luke’s as well.Luke’s age `=` `x` `-5` `=` `20` `-5` Substitute `x=20` `=` `15` Luke is `15` years old.`15` years oldHint
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Question 2 of 5
2. Question
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 oldIrene is (18) years old
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Good Job!
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Help VideoInverse 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,` 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, label the values and form an equation using the information given.Sophia’s age`=x`Irene’s age`=x+4` (since she is `4` years older)Sophia’s age and Irene’s age add up to `32` `x` `+` `x+4` `=` `32` Simplify the equation:`x+x+4` `=` `32` `2x+4` `=` `32` To solve for `x`, it needs to be alone on one side.Start by moving `4` to the other side by subtracting `4` from both sides of the equation.`2``x` `+4` `=` `32` `2``x` `+4` `-4` `=` `32` `-4` `2``x` `=` `28` `4-4` cancels out Next, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `28` `2``x``divide2` `=` `28``divide2` `x` `=` `14` `2divide2` cancels out Substitute `x=14` to get the age of Sophia and Irene.Sophia’s age `=` `x` `=` `14` years old Irene’s age `=` `x` `+4` `=` `14` `+4` `=` `18` years old Sophia is `14` years oldIrene is `18` years oldHint
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Question 3 of 5
3. Question
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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Help VideoInverse 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 oldHint
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Question 4 of 5
4. Question
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 oldHis father is (42) years old
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Well Done!
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Help VideoInverse 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,` 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` Use the information gathered so far to label the values and form an equation.Jack’s age`=x`His father’s age`=x+28` (since he was `28` years old when Jack was born)His father is `3` times as old as Jack `x+28` `=` `3times` `x` Simplify the equation:`x+28` `=` `3timesx` `x+28` `=` `3x` To solve for `x`, it needs to be alone on one side.Start by moving `x` to the other side by subtracting `x` from both sides of the equation.`x` `+28` `=` `3``x` `x` `+28` `-x` `=` `3``x` `-x` `28` `=` `2``x` `x-x` cancels out Next, remove `2` by dividing both sides of the equation by `2`.`28` `=` `2``x` `28``divide2` `=` `2``x``divide2` `14` `=` `x` `2divide2` cancels out `x` `=` `14` Substitute `x=14` to get the age of Jack and his father.Jack’s age `=` `x` `=` `14` years old His father’s age `=` `x` `+28` `=` `14` `+28` `=` `42` years old Jack is `14` years oldHis father is `42` years oldHint
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Question 5 of 5
5. Question
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 oldAlan was (33) years old
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Great Work!
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Help VideoInverse 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,` 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` Use the information gathered so far to label the values and form an equation.Noah’s age`=x`Alan’s age`=6x` (since he `6` times as old as Noah)Alan and Noah’s combined ages is `42` `x+6x` `=` `42` Simplify the equation:`x+6x` `=` `42` `7x` `=` `42` To solve for `x`, it needs to be alone on one side.Remove `7` by dividing both sides of the equation by `7`.`7``x` `=` `42` `7``x``divide7` `=` `42``divide7` `x` `=` `6` `7divide7` cancels out Substitute `x=6` to get Noah and Alan’s age now.Noah’s age `=` `x` `=` `6` years old Alan’s age `=` `6``x` `=` `6(``6``)` `=` `36` years old Finally, subtract `3` from each of their current ages to get Noah and Alan’s age three years ago.Noah’s age `3` years ago `=` `6` `-3` `=` `3` years old Alan’s age `3` years ago `=` `36` `-3` `=` `33` years old Noah was `3` years oldAlan was `33` years oldHint
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