The first step in this problem is to understand what the problem is asking.
Let's use the numbers as variables for now. For example, let use x and y to stand for those numbers. The first part is "the sum of two numbers is 54" so this equation is now x +y = 54
The second part is a little more tricky. as it says "the sum of the smaller and 5 times the larger is 166. Let's use variables again. we can say x+5y=166 (it really doesn't matter which variable you make the larger number). So our two equations are now .
x+y=54
x+5y=166
Does this set-up look familiar? We can now use substitution or elimination method to solve for the x and y and figure out what the two numbers are.
Elimination method means getting rid of a variable in comparison of the two equations vs. substitution is turning one equation into x= or y= and plugging it in the other equation.
For example, in elimination, if I wanted to solve for y, I would eliminate or get rid of x in the equations so I would do something like
-1(x+y=54)
-x-y=-54
and leave the other equation alone
so it would be
-x-y=-54
x+5y=166
adding these two equations would get me
4y=112
and then solve for y
With substitution it goes something like this:
x+y=54
x=54-y
Then substituting it in the other equation would be
(54-y)+ 5y=166 (I used the x=54-y and placed it in the second equation)
You can solve for y in this case as well.
Hope this helps and let me know if something doesn't make sense! :)
