Topics
>
Pre  Algebra>
Equations>
Equation Problems with Substitution>
Equation Problems with Substitution 1Equation Problems with Substitution 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 6 questions completed
Questions:
 1
 2
 3
 4
 5
 6
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
 1
 2
 3
 4
 5
 6
 Answered
 Review

Question 1 of 6
1. Question
Find `w` if the perimeter of the rectangle below is `22` cm. `w=` (4)
Hint
Help VideoCorrect
Good Job!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Perimeter of a Rectangle
`P=2``L` `+2``W`Form an equation using the formula for the Perimeter of a Rectangle.`P=22`cm`L=7`cm`w` cm`P` `=` `2``L` `+2``W` `22` `=` `2(``7``)+2``w` Substitute the values `22` `=` `14+2w` Simplify To solve for `w`, it needs to be alone on one side.Start by moving `14` to the other side by subtracting `14` from both sides of the equation.`22` `=` `14+2w` `22` `14` `=` `14+2w` `14` `8` `=` `2``w` `1414` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`8` `=` `2``w` `8``divide2` `=` `2``w``divide2` `4` `=` `w` `w` `=` `4` Check our workTo confirm our answer, substitute `w=4` to the formed equation.`22` `=` `14+2w` `22` `=` `14+2(4)` Substitute `w=4` `22` `=` `14+8` `22` `=` `22` Since the equation is true, the answer is correct.`w=4` 
Question 2 of 6
2. Question
Find the height `(h)` of the triangle below if its area is `45` cm². (9) cm
Hint
Help VideoCorrect
Excellent!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Area of a Triangle
`A=1/2``b``h`First, label the values and form an equation using the Area of a Triangle formula.`b=10` cm`h=?`cm`A=45`cm²`A` `=` `1/2``b``h` `45` `=` `1/2``10``h` Substitute the values `45` `=` `5h` Simplify To solve for `h`, it needs to be alone on one side.Remove `5` by dividing both sides of the equation by `5`.`45` `=` `5``h` `45``divide5` `=` `5``h``divide5` `9` `=` `h` `5:5` cancels out `h` `=` `9` cm `9` cm 
Question 3 of 6
3. Question
Find the height `(h)` of the trapezium below if `a=7`, `b=9` and its area `(A)` is `72`. `h=` (9)
Hint
Help VideoCorrect
Great Work!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Area of a Trapezium
`A=1/2``h``(``a` `+``b``)`First, label the values and form an equation using the Area of a Trapezium formula.`A=72``a=7``b=9``h=?``A` `=` `1/2``h``(``a` `+``b``)` `72` `=` `1/2``h``(``7` `+``9``)` Substitute the values `72` `=` `1/2 h(16)` Simplify `72` `=` `8h` To solve for `h`, it needs to be alone on one side.Remove `8` by dividing both sides of the equation by `8`.`72` `=` `8``h` `72``divide8` `=` `8``h``divide8` `9` `=` `h` `8:8` cancels out `h` `=` `9` `h=9` 
Question 4 of 6
4. Question
Given that `V=u+at`, find `a` using the following values:`V=178``u=28``t=10` `a=` (15)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, list the values and form an equation using the given formula for `V`.`V=178``u=28``t=10``V` `=` `u` `+a``t` `178` `=` `28` `+a``(10)` Substitute the values `178` `=` `28+10a` Simplify To solve for `a`, it needs to be alone on one side.Start by moving `28` to the other side by subtracting `28` from both sides of the equation.`178` `=` `28+10``a` `178` `28` `=` `28+10``a` `28` `150` `=` `10``a` `2828` cancels out Finally, remove `10` by dividing both sides of the equation by `10`.`150` `=` `10``a` `150``divide10` `=` `10``a``divide10` `15` `=` `a` `10divide10` cancels out `a` `=` `15` `a=15` 
Question 5 of 6
5. Question
Given that `A=(x+y)/2`, find `y` using the following values:`A=51``x=67` `y=` (35)
Hint
Help VideoCorrect
Well Done!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, list the values and form an equation using the given formula for `A`.`A=51``x=67``A` `=` $$\frac{\color{#007DDC}{x}+y}{2}$$ `51` `=` $$\frac{\color{#007DDC}{67}+y}{2}$$ Substitute the values To solve for `y`, it needs to be alone on one side.Start by removing `1/2` by multiplying both sides of the equation by `2`.`51` `=` $$\frac{67+\color{#00880A}{y}}{2}$$ `51``times2` `=` $$\left(\frac{67+\color{#00880A}{y}}{2}\right)\color{#CC0000}{\times2}$$ `102` `=` `67+``y` `1/2times2` cancels out Finally, move `67` to the other side by subtracting `67` from both sides of the equation.`102` `=` `67+``y` `102` `67` `=` `67+``y` `67` `35` `=` `y` `6767` cancels out `y` `=` `35` Check our workTo confirm our answer, substitute `y=35` to the original equation.`51` `=` `(67+y)/2` `51` `=` `(67+35)/2` Substitute `y=35` `51` `=` `102/2` `51` `=` `51` Since the equation is true, the answer is correct.`y=35` 
Question 6 of 6
6. Question
Convert `30°C` to `F` using the formula below:`C=5/9 (F32)` (86)`°F`
Hint
Help VideoCorrect
Excellent!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.First, use the formula and the given value to form an equation.`C=30°``C` `=` `5/9 (F32)` `30` `=` `5/9 (F32)` Substitute `C` To solve for `F`, it needs to be alone on one side.Start by removing `1/9` by multiplying both sides of the equation by `9`.`30` `=` `5/9 (``F` `32)` `30``times9` `=` `5/9 (``F` `32)``times9` `270` `=` `5(``F` `32)` `1/9times9` cancels out Next, remove `5` by dividing both sides of the equation by `5`.`270` `=` `5(``F` `32)` `270``divide5` `=` `5(``F` `32)``divide5` `54` `=` `F` `32` `5divide5` cancels out Finally, move `32` to the other side by adding `32` to both sides of the equation.`54` `=` `F` `32` `54` `+32` `=` `F` `32` `+32` `86` `=` `F` `32+32` cancels out `F` `=` `86°` Therefore, `30°C` is equal to `86°F``86°F`
Quizzes
 One Step Equations – Add and Subtract 1
 One Step Equations – Add and Subtract 2
 One Step Equations – Add and Subtract 3
 One Step Equations – Add and Subtract 4
 One Step Equations – Multiply and Divide 1
 One Step Equations – Multiply and Divide 2
 One Step Equations – Multiply and Divide 3
 One Step Equations – Multiply and Divide 4
 Two Step Equations 1
 Two Step Equations 2
 Two Step Equations 3
 Two Step Equations 4
 MultiStep Equations 1
 MultiStep Equations 2
 Solve Equations using the Distributive Property 1
 Solve Equations using the Distributive Property 2
 Solve Equations using the Distributive Property 3
 Equations with Variables on Both Sides 1
 Equations with Variables on Both Sides 2
 Equations with Variables on Both Sides 3
 Equations with Variables on Both Sides (Fractions) 1
 Equations with Variables on Both Sides (Fractions) 2
 Solve Equations – Variables on Both Sides (Distributive Property) 1
 Solve Equations – Variables on Both Sides (Distributive Property) 2
 Solve Equations – Variables on Both Sides (Distributive Property) 3
 Solve Equations – Variables on Both Sides (Distributive Property) 4
 Writing Equations 1
 Writing Equations 2
 Writing Equations 3
 Writing Equations 4
 Equation Word Problems (Age) 1
 Equation Word Problems (Money) 1
 Equation Word Problems (Harder) 1
 Equation Problems with Substitution 1
 Equation Problems (Geometry) 1
 Equation Problems (Geometry) 2
 Equation Problems (Perimeter)
 Equation Problems (Area)
 Solve for a Variable or Formula 1
 Solve for a Variable or Formula 2
 Solve for a Variable or Formula 3