Solving and Reasoning

Question

Matt took a test consisting of 20 problems. Each correct answer earns 5 points, but each incorrect answer loses 1 point. Matt answered all the questions , and his score was 76. How many questions did he answer correctly?

Answer 1

Let correct answers be x and 5 points is 5x

Let incorrect answers be y and -1 point is -y

5x-y=76

So x+y= 20

Add both equation results in 6x= 96

Divide 6x/6=96/6

X= 16 Y=4

check

5(16)-4=76

16+4=20

Answer 2

x = Number of problems with correct answer

y = Number of problems with incorrect answer

We now have 2 equations:

x+y=20

5x-y=76

--> x=16 --> y=4

So, There are 16 questions that he answered correctly

Please let me know if you have any question and need me to explain more. I will make a video. Thank you