Asked by Celina

I really need help with my math homework today, because I am totally confused! Please give me the answer, but also walk me through it, too, so I can fully understand it, because just the answer won't really help.

#1: A math teacher wants to curve a set of grades. *Just a note, I don't even understand what curve means* She wants to create a formula to turn an old grade, s, into a new grade, t, where t = As + B for some constants A and B. She wants this formula to give a 100 to a student who originally scored 100, and a score of 81 to a student who originally scored 62.

a. How can we view the pairs of original and new scores as points on a line?
b. Use your answer to part a. to determine A and B in the formula.
c. What grade should a student who originally scored 74 receive?

I will post more questions in a little bit. Thank you so much, any help is appreciated, even if you can only answer part of it.

Thanks!
Answered by bobpursley
well, if an original 100 gives a 100

100=A*100+B
and if a 62 is turned into and 81 (magic wand).
81=A*62+B
You have two equations, two unknowns.

First, subtract the second equation from the first.
100-81=A(100-62) And you solve for A.
Then, put that A into either equation and solve for B.
Answered by Celina
Thanks for replying so fast!

Once you got to "subtract the second equation," I got a little confused.

So basically its, 100-81=A(100-63), like you said. Does the B stay put?

And what do you mean by "solve for A" and "put A into either equation?"

Thanks so much!
Answered by bobpursley
When you subtract the second equation fromthe first, you have B-B which is zero, so B disappears.

Solving for A?
100-81=A(100-63),
19=A*37
A=19/37

Now put that into any equation..
100=100A+B
100=100(19/37) + B
B= 100(1-19/37)=100(18/37)
and you have A and B
check my arithmetic
Answered by Celina
Oh, I see... when I got 19/37 when I solved, I thought I was incorrect.

One last thing-- why did you write
B= 100(1-19/37)=100(18/37)? Why did you take away 1?

Thank you!
Answered by bobpursley
100=100(19/37) + B
subtract 100(19/37) from each side.
Answered by Celina
I hate to ask so many questions, but why did you write one, though?

Thanks!
Answered by bobpursley
100-100(19/37)=
100(1-19/37)

It is easier to do this than multiply 100 Times by 19 then divide by 37, then subtract from 100.
Answered by Celina
Thank you so much!
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