One number is 10 times as large as another and their difference is 81. Find the numbers.

one number is 90 and the other one 9

Step-by-step explanation:

Let's refer to the larger number as "x", and the smaller as "y", so we can create equations with those unknowns and solve them algebraically.

Now let's write the first phrase we are given in mathematical form:

"One number is 10 times as large as another one"

Remember that our larger number is "x", so the first equation out of this phrase is:

x = 10 * y

Now for the second phrase:

"Their difference is 81"

Here we need to make the difference setting the larger number first (x), minus the smaller number (y), so as to get a positive difference of 81 units:

x - y = 81

now we solve this system by substituting "x" in the second equation with "10 * y" according to what our first equation states:

10 y - y = 81

9 y = 81

y = 81/9

y = 9

and therefore now that we know the value of number y (9) we can go back to the first equation to find what number "x" is:

x = 10 * (9)

x = 90

Finally: x = 90, and y = 9