Question

If 20 is subtracted from the five times of a number, the obtained subtraction will be 25 more than twice the number

(a) If the number is x, form an equation in the light of the given information and Determine the number
(s) If the obtained number is the sum of three consecutive natural numbers, determine the smallest number.

Answer 1

(a) x = 15

(b) the smallest number is 4.

Explanation:

As per the question If 20 is subtracted from the five times of a number, the obtained subtraction will be 25 more than twice the number.

(a) If the number is x,

Let's form an equation in the light of the given information, The equation becomes,

`\sf 5x - 20 = 2x + 25`

add 20 on both sides

`\sf 5x - 20 + 20 = 25 + 2x + 20`

`\sf 5x = 45 + 2x`

Subtract 2x from both sides,

`\sf 5x - 2x = 45 + 2x - 2x`

`\sf 3x = 45`

Divide both sides by 3,

`\sf x = 15`

Hence the required number is 15.

`\dotfill`

(b) If the obtained number is the sum of three consecutive natural numbers, determine the smallest number.

Let us assume the three consecutive natural numbers be

• x
• x + 1
• x + 2

Adding all the numbers

`\sf x + x + 1 + x + 2 = 15`

`\sf 3x + 3 = 15`

Subtract 3 from both sides

`\sf 3x = 15 - 3`

`\sf 3x = 12`

Divide both sides by 3,

`\sf x = 4`

Therefore the smallest number is 4.

`\dotfill`