1.3. SAT Math: Linear Equations Word Problems

SAT Math is big on real-life word problems, this tests not only your knowledge of the theory about the linear equations, but also your ability to apply that theory.

Here is a process for approaching SAT Math word problem:

• Quickly scan the problem.
  • Decide for yourself if you’re familiar with it enough to spend time on it and attempt solving it, or
  • if it looks like a blob of unknown quantity, then just move on.
• If you decide to pursue solving the problem, go back to the beginning, look for the key information and note it down. The key information that you are looking for are all the things listed below:
  • what is being asked for,
  • the values that are given,
  • unknown quantities,
  • formulas or expressions (if there are any)
  • charts, graphs or tables.
• If you’re still confused with all the information that is given to you, draw a sketch of the problem, remember, a picture is worth a thousand words!
• Start putting together the following:
  • how the key information pieces are related to one another,
  • how they can be put together to figure out what is being asked for (remember all the information to solve the problem is given to you, all you have to do is puzzle it together)
  • what is the independent variable which dictates the outcome of the dependent variable?
  • what is the dependent variable?
  • Note, the units will help you put the expression together or to come up with the solution.
    •  All the terms in the expression have to be expressed in the same units.
      • For example: you can’t add the number of hours to the dollar amounts in the expression, then what do you get?  A mess…
      • If you’re figuring out the cost of a job in ($), and you’re putting all the terms of the expression in ($), then you need to think about how to apply the information given to you that is not in ($) to figure out the needed dollar amounts.  Say, if you multiply the dollar amounts produced from the hours worked, you will get ($) earned, etc.
    • The units can help you figure out what operation to perform.
      • You can figure out many hours someone worked based on the units of other parameters given.  If you were given the total amount of money they made ($) and their hourly rate ($/hr), you can see that if you divide ($) by the rate ($/hr), you will get hours.  In which case this is correct.
• Solve!  And remember, all the information that you need to produce the answer is given to you in the problem.
• If you can’t solve the problem after you spent good amount of time on it, rule out the least probable answers and pick one of the most probable.  Then move onto the next problem.

So without further due, let’s solve some SAT Math linear equation problems!

Example problem 1

Math class students get points for each problem solved in class, which they can exchange for fun stuff at the end of the quarter.  At the beginning of the class each student receives 100 points just for being in class and 25 points for each problem that he solves.  Figure out an expression for points earned per student per day who attend a math class.

First lets put together the key information that is given and that we need to find out:

Given:

100 points at the beginning of the class

25 points per problem 

Find:

Expression for points earned 

Next, to put together an algebraic expression we need to have an independent variable and a dependent variable.

What would be the independent variable, which dictates the outcome of the dependent variable?  The independent variable is usually the key to finding the dependent variable.  It may or may not be given to us explicitly.

The variable that we need for computing the total number of points a student earns is the number of problems a student solves in his math class.  If we don’t have this variable, there is no way we can figure out how many points a student earns in his math class per day.

So, let’s make an independent variable, x, the number of problems a student solves.

Then the dependent variable, y, will be the number of points a student earns per day in math class.

What does the y depend on?

1. Whether the student is in the class (he gets 100 points just for the attendance)
2. How many problems he solves while he’s in the class.  He gets 25 points per x problems)

Now we can put together the expression:

y = 100 + 25x

The answer is y = 25x + 100

Having difficulties with the SAT Math linear equations?  Book a one-on-one session with me or contact me via the contact form above.

Example problem 2

George is an insurance salesman.  His base salary before he makes any sale is $23,000 per year.  For each policy sale, he makes a commission of $65.  Write an equation that will calculate how much money he makes per year based on the amount of sales he makes. 

Having difficulties with the SAT Math linear equations?  Book a one-on-one session with me or contact me via the contact form above.

Example problem 3

A driveway paver uses a function f defined by f(x)=15x+200 to estimate the cost f(x) in dollars to pave a driveway of x square feet.  If the paver estimates that the cost to pave a certain driveway is $2,450, what is the area of the driveway in square feet?

Having difficulties with the SAT Math linear equations?  Book a one-on-one session with me or contact me via the contact form above.