one number is five less another five times the smaller number is one less than the larger number what are the two numbers

Question

that up there was rhe whole question

Answer 1

This problem is actually two separate problems. Lets start by talking about the words in terms of equations. The first unknown number we will call 'x', and the second 'y'. So that means we have

One number:   is     five less       than another number.
x                      =            -5                +y
The next equation is made the same way.
another five     times the smaller number     is     one less     than the larger number
5             *        x                                           =          -1    +y

So that gives us 
x=y-5
and 
5x=y-1

Now we have 2 equations and two unknowns. We can take what we know about one number, and use it to solve for the other number. This process is called substitution. The first equation tells us a different way we can write x. We will use that to write the second equation in a new way.

5 (x) = y-1
becomes
5 (y-5) = y-1

Now we just need to use algebra to solve for y.

First, distribute the 5 on the left.
5(y-5)=y-1
becomes 
5y-25=y-1
-y + 5 y - 25 = -y + y -1
(-y + 5 y) - 25 = (-y + y) -1
4y - 25 = 0 - 1
4y + 25 - 25 = -1 +25
4y +(25 - 25) = (-1 +25)
4y + 0 = 24
4y/4 = 24 / 6
y = 4

Now we know what 'y' (the larger number) is. Remember that we had a way to express 'x' with y.
x = y - 5
We can use what we know about 'y' to get 'x'
x = y -5
x = 4 - 5
x = -1

So y=4 and x = -1 or:
The smaller number is -1,
the larger number is 4.





PS: This problem is what I think you meant, as the question appears to have some typos. I also have tried to be very clear about doing the same thing to both sides of each equation whenever I took a step. I hope this helps.