Greetings, math enthusiasts! In this blog post, we'll embark on a mathematical journey exploring the elegance and practicality of linear functions and equations. Whether you're a student preparing for the SAT exam or someone just eager to understand the fundamentals, this post is your gateway to mastering the art of linear functions and equations.
Here is today's sample SAT math problem. In this problem, we are given two linear functions and are trying to find out what value of the independent variable will give us a break even mark (where the Cost and Revenue equal each other).
SAT Sample Math Problem (Linear Functions/Equations)
The following video link will take you to a video where I explain how to solve this sample problem.
Here are the steps we used to solve the following problem:
Step 1: To find the break-even point, we need to set the cost equal to the revenue and solve for x:
2x+100 = 4x−50
Step 2: Eliminate the variable on one side of the equation. We eliminated the 2x on the left side by subtracting it on both sides.
100 = 2x - 50
Step 3: Eliminate the constant from the right side by adding 50 on both sides of the equation.
150 = 2x
Step 4: Divide both sides of the equation by 2 in order to make the coefficient of x be 1.
75 = x
So, the break-even point occurs when x = 75. Or when 75 units are produced and sold.
Thank you for being part of this mathematical adventure. Let's continue unraveling the beauty of mathematics together!
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