Each multiple choice question: 2 points, each short response question: 4 points
Practice makes perfect
We want to find out how many points each type of question is worth on a practice standardized test. To do so, we will create a system of linear equations and then solve it using the Elimination Method. We will do these things one at a time, starting with forming the system. First, let's take a look at the given table.
You
Your Friend
Multiple Choice
23
28
Short Response
10
5
We will use x to represent the number of points for each multiple choice question and y to represent the number of points for each short response question. From the exercise, we know that we scored a total of 86 points for 23 correct multiple choice questions and 10 correct short response answers. Let's write this as an equation.
23* x+ 10* y= 86Our friend scored a total of 76 for 28 correct multiple choice questions and 5 correct short response answers. Let's write this as an equation, too.
28* x+ 5* y= 76
We can combine these two equations into a system of equations. Let's take a look.
23x+10y=86 & (I) 28x+5y=76 & (II)
Now we are ready to solve this system to find how many points each type of question is worth. Notice that no pair of like terms has the same or opposite coefficients. Let's multiply Equation (II) by 2 so that the y-terms have the same coefficient.
We can subtract Equation (I) from Equation (II) to get an equation in only one variable, x. We also could have multiplied the equation by a negative number and then added the equations — the answer would be the same.
