Answer:
4 questions
Step-by-step explanation:
We can either reason this out with logic or solve it out using a system of equations. I will use a system of linear equations to make it easier to understand. We can use two variables in this case: let x equal the number of questions the team answered correctly, and let y equal the number of questions the team answered incorrectly. Since there are two unknown quantities, we will need two equations. Let's use the fact that there are 50 questions total to create our first equation. The total number of questions is just the sum of the correctly and incorrectly answered questions (assuming the team did not leave any answers blank). This means that our first equation is just the following: x + y = 50. For the purpose of the solution, I am going to isolate y and say that y = 50 - x
We can use the point values were know about to create our second equation. We know that the team got 38 points. We also know that correct answers add one point and incorrect answers subtract two points (meaning incorrect answers are worth twice as much as correct answers). Knowing this, we can set up the following equation: x - 2y = 38 (x number of 1-point questions answered correctly, minus 2 times the number of questions answered incorrectly, equals 38 total points).
The system is the following:
Now, we can use substitution to solve this system of linear equations. We already know that y = 50-x, so let's substitute that into the second equation to solve for x:
y represents the number of questions answered incorrectly, and if we solve for y we get that y = 50 - 46 = 4
Therefore, the team answered 4 questions incorrectly