Equation Problems with Substitution

Question 1 of 6

Find `w` if the perimeter of the rectangle below is `22` cm.

`w=` (4)

Question 2 of 6

Find the height `(h)` of the triangle below if its area is `45` cm².

(9) cm

Question 3 of 6

Find the height `(h)` of the trapezium below if `a=7`, `b=9` and its area `(A)` is `72`.

`h=` (9)

Question 4 of 6

Given that `V=u+at`, find `a` using the following values:

`V=178`

`u=28`

`t=10`

`a=` (15)

Question 5 of 6

Given that `A=(x+y)/2`, find `y` using the following values:

`A=51`

`x=67`

`y=` (35)

Question 6 of 6

Convert `30°C` to `F` using the formula below:

`C=5/9 (F-32)`

(86)`°F`

`P`	`=`	`2``L` `+2``W`
`22`	`=`	`2(``7``)+2``w`	Substitute the values
`22`	`=`	`14+2w`	Simplify

`22`	`=`	`14+2w`
`22` `-14`	`=`	`14+2w` `-14`
`8`	`=`	`2``w`	`14-14` cancels out

`8`	`=`	`2``w`
`8``divide2`	`=`	`2``w``divide2`
`4`	`=`	`w`
`w`	`=`	`4`

`22`	`=`	`14+2w`
`22`	`=`	`14+2(4)`	Substitute `w=4`
`22`	`=`	`14+8`
`22`	`=`	`22`

`A`	`=`	`1/2``b``h`

`45`	`=`	`1/2``10``h`	Substitute the values

`45`	`=`	`5h`	Simplify

Equation Problems with Substitution

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Good Job!

Inverse Operations

Perimeter of a Rectangle

2. Question

Hint

Excellent!

Inverse Operations

Area of a Triangle

3. Question

Hint

Great Work!

Inverse Operations

Area of a Trapezium

4. Question

Hint

Fantastic!

Inverse Operations

5. Question

Hint

Well Done!

Inverse Operations

6. Question

Hint

Excellent!

Inverse Operations

Quizzes

`45`	`=`	`5``h`
`45``divide5`	`=`	`5``h``divide5`
`9`	`=`	`h`	`5-:5` cancels out
`h`	`=`	`9` cm

`A`	`=`	`1/2``h``(``a` `+``b``)`

`72`	`=`	`1/2``h``(``7` `+``9``)`	Substitute the values

`72`	`=`	`1/2 h(16)`	Simplify

`72`	`=`	`8h`

`72`	`=`	`8``h`
`72``divide8`	`=`	`8``h``divide8`
`9`	`=`	`h`	`8-:8` cancels out
`h`	`=`	`9`

`V`	`=`	`u` `+a``t`
`178`	`=`	`28` `+a``(10)`	Substitute the values
`178`	`=`	`28+10a`	Simplify

`178`	`=`	`28+10``a`
`178` `-28`	`=`	`28+10``a` `-28`
`150`	`=`	`10``a`	`28-28` cancels out

`150`	`=`	`10``a`
`150``divide10`	`=`	`10``a``divide10`
`15`	`=`	`a`	`10divide10` cancels out
`a`	`=`	`15`

`A`	`=`	$$\frac{\color{#007DDC}{x}+y}{2}$$

`51`	`=`	$$\frac{\color{#007DDC}{67}+y}{2}$$	Substitute the values

`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

`102`	`=`	`67+``y`
`102` `-67`	`=`	`67+``y` `-67`
`35`	`=`	`y`	`67-67` cancels out
`y`	`=`	`35`

`51`	`=`	`(67+y)/2`

`51`	`=`	`(67+35)/2`	Substitute `y=35`

`51`	`=`	`102/2`

`51`	`=`	`51`

`C`	`=`	`5/9 (F-32)`

`30`	`=`	`5/9 (F-32)`	Substitute `C`

`30`	`=`	`5/9 (``F` `-32)`

`30``times9`	`=`	`5/9 (``F` `-32)``times9`

`270`	`=`	`5(``F` `-32)`	`1/9times9` cancels out

`270`	`=`	`5(``F` `-32)`
`270``divide5`	`=`	`5(``F` `-32)``divide5`
`54`	`=`	`F` `-32`	`5divide5` cancels out

`54`	`=`	`F` `-32`
`54` `+32`	`=`	`F` `-32` `+32`
`86`	`=`	`F`	`-32+32` cancels out
`F`	`=`	`86°`