# Finding a number

**Example 1**

`48` is `25%` of what number?

Multiply both sides by `48` to get `x` on its own (what ever you do to one side you do to the other).

`(4\ \ cancel100times48)/cancel25=(xtimescancel48)/cancel48`

`4times48=x`

`x=4times48`

`x=192`

**Answer:** `48` is `25%` of `192`

**Example 2**

What is `35%` of `26`?

Multiply both sides by `x` to get `x` on its own (what ever you do to one side you do to the other).

`(xtimes100)/35=(26timescancelx)/cancelx`

`(100x)/35=26`

Multiply both sides by `35` to get `x` on its own.

`(100xtimescancel35)/cancel35=26times35`

`100x=26times35`

Divide both sides by `100` to get `x` on its own

`(cancel100x)/cancel100=(26times35)/100`

`x=(26times35)/100`

`x=9.1`

**Answer:** `9.1` is `35%` of `26`

**Example 3**

I’m going to buy `£33.50`, excluding tax, worth of food. The sales tax is `19%`. How much tax do I pay and how much will the total bill be?

This is the same as saying:

What is `19%` of `£33.50`?

Multiply both sides by `x` to get `x` on its own (remember what ever you do to one side you do to the other).

`(100timesx)/19=(33.50timescancelx)/cancelx`

`(100timesx)/19=33.50`

Multiply both sides by `19` to get `x` on its own

`(100xtimescancel19)/cancel19=33.50times19`

`100x=33.50times19`

Divide both sides by 100 to get X on its own

`(cancel100x)/cancel100=(33.50times19)/100`

`x=(33.50times19)/100`

`x=6.37`

**Answer:** The tax is `£6.37` and the total price will therefore be `£6.37 + £33.50 = £39.87`

**Example 4**

A coat costs `£88.00` and is then discounted in a sale by `20%`. How much will the sale price be?

**NOTE:**

With a discount of `20%` the new price is `80%` of the original.

Multiply both sides by `x` to get `x` on its own (what you do to one side you do to the other).

`(100timesx)/80=(88.00timescancelx)/cancelx`

`(100x)/80=88.00`

Multiply both sides by `80` to get `x` on its own.

`(100xtimescancel80)/cancel80=88.00times80`

`100x=88.00times80`

Divide both sides by `100` to get `x` on its own.

`(cancel100x)/cancel100=(88.00times80)/100`

`x=(88.00times80)/100`

`x=70.40`

**Answer:** The sale price will be `£70.40`

# Finding a number

**Example 1**

`48` is `25%` of what number?

Multiply both sides by `48` to get `x` on its own (what ever you do to one side you do to the other).

`(4\ \ cancel100times48)/cancel25=(xtimescancel48)/cancel48`

`4times48=x`

`x=4times48`

`x=192`

**Answer:** `48` is `25%` of `192`

**Example 2**

What is `35%` of `26`?

Multiply both sides by `x` to get `x` on its own (what ever you do to one side you do to the other).

`(xtimes100)/35=(26timescancelx)/cancelx`

`(100x)/35=26`

Multiply both sides by `35 to get `x` on its own.

`(100xtimescancel35)/cancel35=26times35`

`100x=26times35`

Divide both sides by `100` to get `x` on its own

`(cancel100x)/cancel100=(26times35)/100`

`x=(26times35)/100`

`x=9.1`

**Answer:** `9.1` is `35%` of `26`

**Example 3**

I’m going to buy `£33.50` excluding tax worth of food. The sales tax is `19%`. How much tax do I pay and how much will the total bill be?

This is the same as saying:

What is `19%` of `£33.50`?

Multiply both sides by `x` to get `x` on its own (remember what ever you do to one side you do to the other).

`(100timesx)/19=(33.50timescancelx)/cancelx`

`(100timesx)/19=33.50`

Multiply both sides by `19` to get `x` on its own

`(100xtimescancel19)/cancel19=33.50times19`

`100x=33.50times19`

Divide both sides by 100 to get X on its own

`(cancel100x)/cancel100=(33.50times19)/100`

`x=(33.50times19)/100`

`x=6.37`

**Answer:** The tax is `£6.37` and the total price will therefore be `£6.37 + £33.50 = £39.87`

**Example 4**

A coat costs `£88.00` and is then discounted in a sale by `20%`. How much will the sale price be?

**NOTE:**

With a discount of `20%` the new price is `80%` of the original.

Multiply both sides by `x` to get `x` on its own (what you do to one side you do to the other).

`(100timesx)/80=(88.00timescancelx)/cancelx`

`(100x)/80=88.00`

Multiply both sides by `80` to get `x` on its own.

`(100xtimescancel80)/cancel80=88.00times80`

`100x=88.00times80`

Divide both sides by `100` to get `x` on its own.

`(cancel100x)/cancel100=(88.00times80)/100`

`x=(88.00times80)/100`

`x=70.40`

**Answer:** The sale price will be `£70.40`