Question

One number is bigger than another by 406. If the bigger number is divided by the smaller one, you’ll get the quotient 3 and remainder 66. Find the numbers.

Answer 1

By solving a system of equations we will see that the two numbers are 576 and 170.

How to find the numbers?

Let's say that x is the larger number and y is the smaller one.

We know that:

x - y = 406

And:

(x - 66)/y = 3

(if we remove the remainder from the original number, the quotient is just 3).

So we have a system of equations, by isolating y on the first equation we get:

y = x - 406

Replacing that in the quotient we get:

(x - 66)/(x - 406) = 3

We can solve this for x:

x - 66 = 3*(x - 406)

x - 66 = 3x - 3*406

3*406 - 66 = 3*x - x

(3*406 - 66)/2 = x = 576

And the value of y is given by:

y = x - 406 = 576 - 406 = 170

So the two numbers are 576 and 170.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904