I'm having trouble figuring out this question on one of my son's sheets.

Question

"Mrs. Sneel's math test has twenty questions and is worth 100 points. The test consists of multiple choice questions worth 3 points each and short answer questions worth 11 points each. How many multiple choice questions are on the test?" and "If a passing score on the test is 70 points or greater, what is the minimum number of questions you can get correct and still pass the test?" are the questions, but I'm quite clueless of how to solve them, we got one equation for them, but nothing else. I might just not be thinking right, but my son and I are stumped.

Answer 1

The second part depends on which questions you get right.

You can get 5 11's and 5 3's for a total of 70.

You can get 4 11's and 9 3's for a total of 71.

You can get 3 11's and 13 3's for a total of 72.

 

Answer 2

Let x = the number of multiple choice questions

20 - x = the number of short answer questions

 

3x + 11(20 - x) = 100

3x + 220 - 11x = 100

-8x = -120

x = 15

 

There are 15 multiple choice and 20 - 15 = 5 short answer questions

 

Answer 3

Hi Jonathan,

 

Let the number of multiple choice questions be x and short answer questions be y.

x + y = 20

3x + 11y = 100 (I wrote this equation based on the score values of the questions)

Now, I will use elimination to find one of the variables. To do that, I will multiply the first equation by -3 and then add them up.

-3(x + y = 20)
3x + 11y = 100

 

-3x - 3y = -60

3x + 11y = 100

+------------------

 8y = 40

y = 5 (number of short answer questions)

x + y = 20

20 - 5 = x

x = 15 (number of multiple choice questions)

 

If the passing score is 70 or greater, and you need to answer minimum number of questions to get this, you need to answer all the short assay questions first which will earn you 5*11 = 55 points

we still need 70 - 55 = 15 points, which is worth 5 multiple choice questions 3*5 = 15 points

5 + 5 = 10 is the minimum number of questions to be answered to pass with a score of 70

 

Answer 4

Hi Johnathan,

 

I'd like to help you to figure out.

 

Suppose there are X multiple choice questions and Y short answer questions,

 

Therefore, total points for multiple choice questions would be 3 X, and total points for short answer questions would be 11 Y.

 

We can set up the system equation:

 

X + Y = 20 (Total questions)

3 X + 11 Y = 100 (Total points)

 

First equation multiply 3, it would become: 3 X + 3 Y = 60

And then subtract, 8 Y = 40

and then divide by 8, Y = 5 

 

Next we can figure out how much short answer questions, plug Y = 5 into X + Y =20, we would get X = 15

It means: there are 15 multiple choice questions and 5 short answer questions.

 

 

Answer 5

Let's assume there is X number of Multiple Choice questions and Y number of Short Answer questions.

 

There are 20 questions in total, so X + Y = 20 --> Equation 1

 

Also, 3 points for Multiple Choice questions means total of 3*X points, and 11 points for Short Answer questions, which means 11*Y points. Now we have 3*X + 11*Y = 100 points --> Equation 2

 

If we solve these two equations:

(a) Multiply equation 1 by 3 on both sides to give 3*X + 3*Y = 3*20

(b) Subtract equation above from equation 2 will cancel out X and we will have 8*Y = 40.

(c) Therefore, Y = 5. 

(d) Substitute value of Y in equation 1 and get X = 15.

 

Ensure you have got the right answers by substituting the values of X and Y in equation 1 and 2 and see it matches.

 

Hope this helped.