Question

The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number. Find the numbers.

Answer 1

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Explanation:

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Answer 2

Let the smaller number be x.

Given, the larger number is 7 times the smaller number.

So, the larger number = 7x.

Given, 3 times the larger number is 7 more than 4 times the smaller number.

So we can write the equation as,

`3(7x) = 4(x)+7`

`3(7x) = 4x+7`

`21x = 4x+7`

Now we have to move 4x to the left side by subtracting 4x from both sides.

`21x-4x = 4x-4x+7`

`21x-4x = 7`

`17x = 7`

To get x, we will divide both sides by 17. We will get,

`(17x)/(17) = (7)/(17)`

`x = (7)/(17)`

So the smaller number =
`(7)/(17)`

The larger number =
`7((7)/(17) )` =
`(49)/(17)`

So we have got the required numbers.

Smaller number =
`(7)/(17)` and larger number =
`(49)/(17)`.