SOLUTION: Amy has a $50 note and a $20 note. She exchanged all the money for a total number of 23 $2 coins and $5 coins. How many $5 coins does she get?

The total is 50 + 20 = 70 dollars.

So, if x and y are the numbers of 2-dollar coins and 5-dollar coins respectively,
we can write these two equations


     x +  y = 23        (1)    (counting coins)
    2x + 5y = 70        (2)    (the total)


Now, there are different methods to solve this system.

The beginners usually use the substitution method, since it is simpler to understand.


So, using this method, express from equation (1)  x = 23-y  and substitute it into equation (2), replacing x there.

You will get a single equation for y

    2*(23-y) + 5y = 70.


Simplify it step by step and solve for y.


    46 - 2y + 5y = 70

    3y = 70 - 46

    3y = 24  ====>  y = 24/3 = 8.


Answer.  8 5-dollar coins and the rest, 23-8 = 15 of the 2-dollar coins.


CHECK.   8*5 + 15*2 = 40 + 30 = 70 dollars total.   ! Precisely correct !