Question

SAT: if a + b = s and a - b = t then which of the following expresses the value of ab in terms of s and t

Answer 1

st
(s-t)/2
(s+t)/2
(s^2-t^2)/4
(s^2-t^2)/2

Answer 2

If we solve for a and b in terms of s and t, we can simply multiply the values of a and b together to get the expression...

Note that if we pretend s and t are just constants, we basically just have a system of linear equations:
a + b = s like x + y = constant
a - b = t like x - y = constant

Answer 3

@AccessDenied I'm still a bit confused

Answer 4

Well, how would you go about solving something like this:
x + y = 6
x - y = 2
We could do substitution or elimination or perhaps some other method.
In the same regards,
a + b = s
a - b = t
We could do the same thing, except the only difference will be that we have s and t instead of numbers being manipulated. For example, in the first set, we could solve for x by elimination:
x + y = 6
x - y = 2
-----------
2x = 8
x = 4

How about doing the same for a in the second:
a + b = s
a - b = t
----------------
2a + 0 = s + t
2a = s + t
a = (s + t)/2

Can you see how that parallels the first situation?

Answer 5

@AccessDenied Thank you :-)

Answer 6

You're welcome! :)
Did you find your answer?

Answer 7

(s^2-t^2)/4?

Answer 8

@AccessDenied

Answer 9

Yes, that is what I got as well. Great! :D

Answer 10

Strategy:
(1) Solve both equations for the variable a.
(2) Add those two equations.

(3) Solve both equations for the variable b.
(4) Add those equations.

(5) Multiply the result of step (2) by the result of step (4)

(6) Simplify to get ab.

Let's see if this works.

Answer 11

@Directrix Haha, a little bit late, right? :P

Answer 12

I am doing this for my own practice. Better late than never. :)

Answer 13

@Directrix Haha, glad to see you on here again

Answer 14

1) a = s - b
a = t + b
-----------
2) 2a = s + t *

3) b = s - a
b = a - t
-------------
4) 2b = s - t **

5) (2a = s + t *) times (2b = s - t **)

4ab = (s + t) times (s - t)
4ab = (s² - t²)
ab = (s² - t²) / 4 --> 4th option

Answer 15

Are you practicing for the SAT as well?

Answer 16

Always. The SAT math is a different way of thinking than that we learn in math class. The SAT is more aptitude-oriented - an AHA, moment.

Answer 17

@Directrix Oh, do you mind if I ask how old you are? I've always thought you were middle aged for some reason hahah

Answer 18

I don't mind if you ask. I'm just not telling; at least, not tonight. :)