Help with math project

Question

This my son's math project.  I really want him to get an A.  The question is as follows:

 

A student earns 13 points for every correct answer and loses 7 points for every wrong answer on a quiz. Oliver takes the quiz and answer all 40 questions and earns 60 points. How many did he answer correctly?

Answer 1

Hi Angela, we can set up a system of equations to solve this problem. Let x be the number of correct answers and y be the number of incorrect answers. We know the number of questions on the quiz is 40. Then:

 

x + y = 40

 

We also know the score on the quiz is 60. For each correct answer the student received 13 points and for each incorrect answer he lost 7 points, Then:

 

13 * x - 7 * y = 60

 

Solve:

 

   x  +    y  =  40

13x  -  7y  =  60

-------------------

 

Multiply the first equation by 7 and add:

 

  7x + 7y = 280
13x  - 7y =   60
-------------------

 

20x         = 340

 

Divide both sides by 20:

 

x = 17

 

The student answered 17 questions correctly. 

 

Using the first equation, we can find out how many questions were incorrect.

 

x  +  y  = 40

 

17 + y  = 40

 

Subtract 17 from both sides:

 

y = 23

 

The student answered 23 questions incorrectly.

 

Check:

 

Use the second equation to check the answers.

 

17 * 13 - 23 * 7 = 60

 

221 - 161 = 60

 

60 = 60, values check.

 

Questions?

 

Answer 2

x=# of correct answers

y=# of wrong answers

13x-7y=60

x+y=40

x=40-y

substitute

13(40-y)-7y=60

520-13y-7y=60

520-20y=60

-20y=60-520

-20y=-460

20y=460

2y=46

y=46/2

y=23 wrong answers

x+23=40

x=40-23

x=17 correct answers

13*17-7*23=221-161=60