Equation Word Problems 2
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Question 1 of 5
1. Question
The product of `3` and `a` is divided by `4` and is equal to twice the sum of `a` and `10`. Solve for `a`.- `a=` (-16)
Hint
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Excellent!
Incorrect
Inverse 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, form an equation using the information given.The product of `3` and `a` is divided by `4` and is equal to twice the sum of `a` and `10` `3timesa` `divide` `4` `=` `2times` `a+10` Simplify the equation:`(3timesa)divide4` `=` `2times(a+10)` `(3a)/4` `=` `2(a+10)` To solve for `a`, it needs to be alone on one side.Start by removing `1/4` by multiplying both sides of the equation by `4`.$$\frac{3\color{#00880A}{a}}{4}$$ `=` `2(``a` `+10)` $$\frac{3\color{#00880A}{a}}{4}\color{#CC0000}{\times4}$$ `=` `2(``a` `+10)``times4` `3``a` `=` `8(``a` `+10)` `1/4times4` cancels out Next, expand the right side of the equation using the Distributive Property.`3``a` `=` `8``(``a` `+10)` `3``a` `=` `8``a` `+``8``(10)` `3``a` `=` `8``a` `+80` Now, move `8a` to the other side by subtracting `8a` from both sides of the equation.`3``a` `=` `8``a` `+80` `3``a` `-8a` `=` `8``a` `+80` `-8a` `-5``a` `=` `80` `8a-8a` cancels out Finally, remove `-5` by dividing both sides of the equation by `-5`.`-5``a` `=` `80` `-5``a``divide-5` `=` `80``divide-5` `a` `=` `-16` `-5divide-5` cancels out `a=-16` -
Question 2 of 5
2. Question
`3` times a number plus `7` is the same as `5` times the number minus `9`. What is the number?- (8)
Hint
Help VideoCorrect
Great Work!
Incorrect
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.Number`=n``3` times a number plus `7` is the same as `5` times the number minus `9` `3` `times` `n` `+` `7` `=` `5` `times` `n` `-` `9` Simplify the equation:`(3timesn)+7` `=` `(5timesn)-9` `3n+7` `=` `5n-9` To solve for `n`, it needs to be alone on one side.Start by moving `3n` to the other side by subtracting `3n` from both sides of the equation.`3``n` `+7` `=` `5``n` `-9` `3``n` `+7` `-3n` `=` `5``n` `-9` `-3n` `7` `=` `2``n` `-9` `3n-3n` cancels out Next, move `9` to the other side by adding `9` to both sides of the equation.`7` `=` `2``n` `-9` `7` `+9` `=` `2``n` `-9` `+9` `16` `=` `2``n` `-9+9` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`16` `=` `2``n` `16``divide2` `=` `2``n``divide2` `8` `=` `n` `2divide2` cancels out `n` `=` `8` The number is `8`.Check our workTo confirm our answer, substitute `n=8` to the original equation.`3n+7` `=` `5n-9` `3(8)+7` `=` `5(8)-9` Substitute `n=8` `24+7` `=` `40-9` `31` `=` `31` Since the equation is true, the answer is correct.`8` -
Question 3 of 5
3. Question
A number divided by `4` plus `6` equals twice the number minus `15`. What is the number?- (12)
Hint
Help VideoCorrect
Well Done!
Incorrect
Inverse 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, label the values and form an equation using the information given.Number`=x`A number divided by `4` plus `6` equals twice the number minus `15` `x` `divide` `4` `+` `6` `=` `2times` `x` `-` `15` Simplify the equation:`(xdivide4)+6` `=` `(2timesx)-15` `x/4 +6` `=` `2x-15` To solve for `x`, it needs to be alone on one side.Start by removing `1/4` by multiplying both sides of the equation by `4`.$$\frac{\color{#00880A}{x}}{4}+6$$ `=` `2``x` `-15` $$\left(\frac{\color{#00880A}{x}}{4}+6\right)\color{#CC0000}{\times4}$$ `=` `(2``x` `-15)``times4` `x` `+24` `=` `4(2``x` `-15)` `1/4times4` cancels out Next, expand the right side of the equation using the Distributive Property.`x` `+24` `=` `4``(2``x` `-15)` `x` `+24` `=` `4``(2``x``)+``4``(-15)` `x` `+24` `=` `8``x` `-60` Now, move `x` to the other side by subtracting `x` from both sides of the equation.`x` `+24` `=` `8``x` `-60` `x` `+24` `-x` `=` `8``x` `-60` `-x` `24` `=` `7``x` `-60` `x-x` cancels out Then, move `60` to the other side by adding `60` to both sides of the equation.`24` `=` `7``x` `-60` `24` `+60` `=` `7``x` `-60` `+60` `84` `=` `7``x` `-60+60` cancels out Finally, remove `7` by dividing both sides of the equation by `7`.`84` `=` `7``x` `84``divide7` `=` `7``x``divide7` `12` `=` `x` `7divide7` cancels out `x` `=` `12` The number is `12`.`12` -
Question 4 of 5
4. Question
The sum of a number and `6` when multiplied by `4` equals `3` times the sum of `9` and that number. What is the number?- (3)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Inverse 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, label the values and form an equation using the information given.Number`=x`The sum of a number and `6` when multiplied by `4` equals `3` times the sum of `9` and that number `x+6` `times` `4` `=` `3times` `9+x` Simplify the equation:`(x+6)times4` `=` `3times(9+x)` `4(x+6)` `=` `3(9+x)` To solve for `x`, it needs to be alone on one side.Start by expanding both sides of the equation by using the Distributive Property.`4``(``x` `+6)` `=` `3``(9+``x``)` `4``x` `+``4``(6)` `=` `3``(9)+``3``x` `4``x` `+24` `=` `27+3``x` Now, move `3x` to the other side by subtracting `3x` from both sides of the equation.`4``x` `+24` `=` `27+3``x` `4``x` `+24` `-3x` `=` `27+3``x` `-3x` `x` `+24` `=` `27` `3x-3x` cancels out Finally, move `24` to the other side by subtracting `24` from both sides of the equation.`x` `+24` `=` `27` `x` `+24` `-24` `=` `27` `-24` `x` `=` `3` `24-24` cancels out The number is `3`.Check our workTo confirm our answer, substitute `x=3` to the original equation.`4(x+6)` `=` `3(9+x)` `4(3+6)` `=` `3(9+3)` Substitute `x=3` `4(9)` `=` `3(12)` `36` `=` `36` Since the equation is true, the answer is correct.`3` -
Question 5 of 5
5. Question
`24` plus `3` times a number equals `4` divided into the sum of 7 times the number plus `1`. What is the number?- (-19)
Hint
Help VideoCorrect
Good Job!
Incorrect
Inverse 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, label the values and form an equation using the information given.Number`=n``24` plus `3` times a number equals `4` divided into the sum of 7 times the number plus `1` `24` `+` `3` `times` `n` `=` `[(7timesn)+1]divide4` Simplify the equation:`24+(3timesn)` `=` `[(7timesn)+1]divide4` `24+3n` `=` `(7n+1)/4` To solve for `n`, it needs to be alone on one side.Start by removing `1/4` by multiplying both sides of the equation by `4`.`24+3``n` `=` $$\frac{7\color{#00880A}{n}+1}{4}$$ `(24+3``n``)``times4` `=` $$\frac{7\color{#00880A}{n}+1}{4}\color{#CC0000}{\times4}$$ `4(24+3``n``)` `=` `7``n` `+1` `1/4times4` cancels out Next, expand the left side of the equation using the Distributive Property.`4``(24+3``n``)` `=` `7``n` `+1` `4``(24)+``4``(3``n``)` `=` `7``n` `+1` `96+12``n` `=` `7``n` `+1` Now, move `7n` to the other side by subtracting `7n` from both sides of the equation.`96+12``n` `=` `7``n` `+1` `96+12``n` `-7n` `=` `7``n` `+1` `-7n` `96+5``n` `=` `1` `7n-7n` cancels out Then, move `96` to the other side by subtracting `96` from both sides of the equation.`96+5``n` `=` `1` `96+5``n` `-96` `=` `1` `-96` `5``n` `=` `-95` `96-96` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``n` `=` `-95` `5``n``divide5` `=` `-95``divide5` `n` `=` `-19` `5divide5` cancels out The number is `-19`.Check our workTo confirm our answer, substitute `n=-19` to the original equation.`24+3n` `=` `(7n+1)/4` `24+3(-19)` `=` `(7(-19)+1)/4` Substitute `n=-19` `24-57` `=` `(-133+1)/4` `-33` `=` `(-132)/4` `-33` `=` `-33` Since the equation is true, the answer is correct.`-19`
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