Jim has received scores of 74and 80 on his first two 100 point tests. What score must he get on his third 100 point test to keep an average of 83 or greater?

Third test = 'blank' (If the average is greater then the possible number of points, enter DNE)

Question

Jim has received scores of 74and 80 on his first two 100 point tests. What score must he get on his third 100 point test to keep an average of 83 or greater?

Third test >= 'blank' (If the average is greater then the possible number of points, enter DNE)

anonymous · Answer

Ok, so (74 + 80 + x)/3 = 83 - does that make sense?

myininaya · Answer

inequality

anonymous · Answer

So do I divide the three then?

anonymous · Answer

You're right myin, but since we know the limit, 100 - aren't we just finding the minimum number that will give you an 83 average? Or am I reading/doing this wrong?

anonymous · Answer

Lulu, you multiply both sides of the equation by 3

anonymous · Answer

(Which gets rid of the /3 portion on the left)

anonymous · Answer

the answer doesn't have to be 83, it can be a higher average

myininaya · Answer

we want the average to be greater than or equal to 83
so we have
$$\frac{74+80+x}{3} \text { is the average } $$
we want
$$\frac{74+80+x}{3}  \text{ we want this to be greater than or equal to 83} $$
symbolically this looks like
$$\frac{74+80+x}{3} \ge 83 $$

myininaya · Answer

but once you get x=100
you could have also wrote x>=100 in the end
so your way would have worked fine
i just like my equations/inequalities read like my sentences

myininaya · Answer

that was an example by the way with the x=100

myininaya · Answer

i didn't solve this sorry lol

anonymous · Answer

So, I have a question that might be a bit silly. How do I work with the division of the equation. For the life of me I can't remember how to work an equation like that.

anonymous · Answer

Hey lulu - sorry I stepped away for a bit - so your question is regarding how to deal with the division of the equation?

anonymous · Answer

Yes, I'm not sure how to do it. Haven't covered it in a while and I can't remember how to go about it.

anonymous · Answer

No problem! So, the rule of thumb is when you multiply/divide, you need to do the same thing to both sides of the equation.

anonymous · Answer

So, in our case, you want to multiply both sides of the equation by 3, like this:

$$(74 + 80 + x)/3 *3 = 83 * 3$$

anonymous · Answer

Oooh I get it, thank you so much!

anonymous · Answer

Awesome - thanks for sticking with me, I got confused myself there for a bit :P. And sorry for going quiet for a bit there - great work lulu, thanks!