Math, asked by shayan61, 1 year ago

four - fifths of a number is 10 more than two - thirds of the number. find the number

Answers

Answered by pinakimandal53

Let the number be $x$ .

Four-fifths of a number is 10 more than two-thirds of the number
⇒ Four-fifths of a number = 10 more than two-thirds of the number
⇒ $\frac{4}{5}x = \frac{2}{3}x + 10$
Multiplying both sides of the equation by 15.
⇒ $12x = 10x + 150$
⇒ $12x - 10x = 150$
⇒ $2x = 150$
⇒ $\frac{2x}{2} = \frac{150}{2}$ [Dividing both sides of the equation by 2. ]
⇒ $x = 75$
∴ The number is 75.

Hope this may help you.

If you have any doubt, then you can ask me in the comments.

shayan61: Why are we multiplying them with 15

shayan61: Why are we multiplying them by 15

pinakimandal53: We are multiplying both sides of the equation by 15 to remove the denominators.

pinakimandal53: 15 is the LCM of the denominators 3 and 5.

pinakimandal53: Any further doubts?

pinakimandal53: If we multiply 4/5 x by 15, then we get 12x.

pinakimandal53: Sorry, the number is 75, not 5.

pinakimandal53: If we multiply whole (2/3 x + 10) by 15, then using the 'distributive property of multiplication', we get (10x + 150).

shayan61: Thanks alot

pinakimandal53: You're welcome. I hope you understood this logically.

Answered by XxFantoamDEADPOOLXx

Answer:

Let the number be x .

Four-fifths of a number is 10 more than two-thirds of the number

•Four-fifths of a number = 10 more than two-thirds of the number.

• $\frac{4}{5} x = \frac{2}{3} x + 10$

•Multiply both sides by cross multiplication method.

•12x = 10x + 150

•12x - 10x = 150

• $2x = 150$

• $x = \frac{150}{2}$

•X=75

The number is 75.

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