We can define two variables:
x = large number
y = small number
Now, set up a system of equations:
[tex]x + y = 45[/tex]
[tex]4y = x[/tex]
Solve the system. I'm going to use the second equation to substitute 'x' into the first one (x = 4y):
[tex]4y + y = 45[/tex]
[tex]5y = 45[/tex]
[tex]y = 9[/tex]
Plug that back into 2nd equation to find both numbers:
[tex]4y = x[/tex]
[tex]4(9) = x = 36[/tex]
So, x = 36 and y = 9.
We can check. 36 + 9 actually does equal 45 and 4 times 9 is 36. We match our initial criteria, so our answer is right.
