Write and solve an inequality How do I write and solve an inequality like this: Ryan had  70 pieces of candy. Every day at lunch, he ate a piece and gave a piece to each of his three friends. What is the number of days and 20 pieces of candy left?
 A: Denote by $c(n)$ the number of pieces of candy Ryan has at the end of day $n$. Define, according to the given conditions,
$$
c(0)=70, \quad
c(n) = 70 - 4n.
$$
It turns out that at the end of day 12 Ryan has 22 pieces of candy left; at the end of day 13 Ryan has only 18 pieces of candy left. We can find this by solving these simultaneous inequalities:
$$
70-4d\ge20,
$$
$$
70-4(d+1)<20.
$$
Here day $d$ is the last day when Ryan has at least 20 pieces of candy left.
From these inequalities we indeed find $$d=12.$$
Day 12 is the last day when Ryan has at least 20 pieces of candy (at the end of the day).
A: Well, first idetify what variables you want to solve.  You want to know how many days until something happens.  So the first thing to do is:
Let $x =$ the number of days when the number of candy is 20.
Now that is the only variable needed and we can set this problem up to solve just one equation in terms of this variable.  But, in my opinion, this is too hard and it is easy to make another variable for the number of candies.  Must people will balk at this an assume solving two equations with two variables is harder but I think that is a misconception.  It's harder to set up an equation exactly with just one.
So I'd say.  Let $y =$ the number of candies left.
So now we need to find the relation between them.
"Each day he at a piece" so after $x$ days he ate $x$ pieces.  "and gave 3 away" so after $x$ days he gave away $3x$ pieces  So how many are left?  He started with $70$ and after $x$ days he got rid of $x + 3x$ pieces so the amount of candy left is $70 -(x + 3x)$ after $x$ days.
So $y = 70 - (x + 3x)$.  And we want $y= 20$.  
So $20 = 70-(x+3x)$.  What can $x$ be?
