Stuck on a story problem

Question

I'm the teacher, and I'm stuck.... 

The difference between two numbers is 12. If 20 is added to twice the larger number, the result is 4 more than 3 times the smaller number. Find the two numbers.

Answer 1

first, assign variables (unknowns)---let's use X and Y, and let Y be the larger number.

 

next, write equations to match what is described:

 

The difference between two numbers is 12:

    Y - X = 12

 

20 is added to twice the larger number, the result is 4 more than 3 times the smaller number

     2Y + 20 = 3x + 4

 

Now you have 2 equations in two unknowns---these can be solved using substitution or "elimination".  For example, the first equation can be rewritten as:

Y = X + 12

Now you can substitute X + 12 in place of Y in the second equation.