Question

You and three friends decide to go to the fair. The cost for parking is three dollars. Admission is 12 dollars per person. If you have 155 dollars, what is the maximum amount each person can spend on food? Write and solve an inequality.

Answer 1

Let the variable f represent the amount of money that each person can spend on food.

We shall start by placing the total amount of dollars you have on the left side of the inequality.  This has to be less than or equal to the number of dollars that you and your group of friends spends, because you can't spend more money than you have ;) 

Also, on the right side of the inequality, we know that you and your friends spend 3 dollars, because that is how much parking costs.  In addition to this, we have admission, which costs 12 dollars per person, and there are 4 people in your group. 12*4=48, which is the total cost of admission for your group.  Finally, you need to add the cost of food to this side of the inequality, which is the same for each person in your 4 person group.  This can be represented by the expression 4f.

So, if we write this inequality, it would be:

155≤ 3 + 48 + 4f

If we simplify the right side of the inequality, by combining like terms, we get the simplified inequality:
155 ≤ 51 + 4f

To further simplify this inequality, we must keep all of the integers on the left side, in attempt to get the variable alone on the right side.  To do this, we must subtract 51 from both sides of the inequality, to get:

104 ≤ 4f

Finally, we must divide both sides of the inequality by 4, because it is the coefficient of f, and that is the variable that we are trying to get alone.

26 ≤ f

This means that you and each of your friends can only spend 26 dollars each on food.