Question #8e191

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!

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.