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!

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.

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!

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

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!

100=100(19/37) + B

subtract 100(19/37) from each side.

I hate to ask so many questions, but why did you write one, though?

Thanks!

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.

Thank you so much!

No problem! I'm here to help you understand the concept. Let's start with the first question:

#1: To understand how to curve grades, let's break it down step by step.

a. To view the pairs of original and new scores as points on a line, we can create a coordinate system with the original scores on the x-axis and the new scores on the y-axis. Each pair of original and new scores represents a point on this line. For example, if a student originally scored 70 and the new score is 85, that would be represented as the point (70, 85) on the coordinate system.

b. Now, let's determine A and B in the formula. Given that a score of 100 should map to a new score of 100, we can plug in these values into the formula t = As + B. So, 100 = A * 100 + B. Similarly, with the other data point, 81 = A * 62 + B.

To solve for A and B, we have a system of two equations:

Equation 1: 100 = A * 100 + B
Equation 2: 81 = A * 62 + B

We can solve this system by either substitution or elimination. Let's use substitution:

From Equation 1, we can isolate B:
B = 100 - A * 100

Now, substitute this value of B into Equation 2:
81 = A * 62 + (100 - A * 100)

Simplify the equation:
81 = A * 62 + 100 - A * 100

Combine like terms:
81 = 62A + 100 - 100A

Simplify further:
81 = 38A + 100

Bring 100 to the left side:
81 - 100 = 38A
-19 = 38A

Divide both sides by 38:
A = -19/38
A = -0.5

Now substitute the value of A back into Equation 1 to solve for B:
100 = (-0.5) * 100 + B

100 = -50 + B

Bring -50 to the left side:
100 + 50 = B
150 = B

So, A = -0.5 and B = 150.

c. To find the grade a student who originally scored 74 should receive, we can use the formula t = As + B.
Plugging in the values of A and B we found in step b, we get:

t = (-0.5) * 74 + 150

Simplifying:
t = -37 + 150
t = 113

Therefore, a student who originally scored 74 should receive a grade of 113.

I hope this explanation helps you understand the process of curving grades and how to derive the values of A and B! Let me know if you have any further questions.