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

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,

$\frac{17x}{17} = \frac{7}{17}$

$x = \frac{7}{17}$

So the smaller number = $\frac{7}{17}$

The larger number = $7(\frac{7}{17} )$ = $\frac{49}{17}$

So we have got the required numbers.

Smaller number = $\frac{7}{17}$ and larger number = $\frac{49}{17}$.