Question #8e191

2 Answers
Joshua Z.
Nov 23, 2017

2 correct multiple choice
9 correct fill-in

Explanation:

Okay, let's start by defining our variables:

#m=# number of correct multiple choice

#f=# number of correct fill-in

The first equation we can write uses the fact that there are 11 correct answers:

#m+f=11#

#f=11-m#

Now, we can write another equation uses the number of points. Since multiple choice questions are 10 points each and fill-in questions are 14 points each, we have:

#10m+14f=146#

We know what #f# is equal to in terms of #m#:

#10m+14(11-m)=146#

#10m+154-14m=146#

#154-146=14m-10m#

#4m=8#

#m=2# correct multiple choice

So there are 2 correct multiple choice answer. It's easy to find the number of correct fill-in answers:

#f=11-m=11-2=9# correct fill-in

We can check our work:

#2*10+9*14=20+126=146#

So, our answer is correct and makes sense. Hope this helps!

Ratnaker Mehta
Nov 23, 2017

#2# multiple-choice and #9# fill-in questions were answered

correctly.

Explanation:

Suppose that, multiple-choice questions answered correctly are

#m#, which yield a score of #10m# points.

Total no. of correct answers is #11,# out of which #m# are multiple-

choice, so, the no. of fill-in correctly answered questions is

#(11-m),# giving a score of #14(11-m)# points.

Thus, total score of points becomes, #10m+14(11-m).#

But we are given that this score is #146# points.

#:. 10m+14(11-m)=146.#

#:. 10m+154-14m=146.#

#:. -4m=146-154=-8.#

#:. m=-8/-4=2, and, :., 11-m=11-2=9.#

Thus, #2# multiple-choice and #9# fill-in questions were answered

correctly.

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