Have you tried "Rule #1"?
W = how many of the 2500 calls were made by females
x = Success Rate of Females
M = how many of the 2500 calls were made by males
n = Success Rate of Males
What do we know? How do we express it in terms of these names?
Note: There are other ways to do this. This is one way that makes sense to me and might make sense to you.
"in 2500 phone calls"
W + M = 2500
"twice as many sales per call with a woman's vaoice than with a man's voice"
x = 2*n
"360 resulted in sales and were made by male callers"
M*n = 360
"480 resulted in sales and were made by female callers"
W*x = 480
There will be some flag-waving, here. I defined FOUR variables!!! Please, do NOT let that scare you. Just solve it the way it is. Gather things up and ponder the pile. The advantage in having names and expressions is that we can now simply ignore the narrative and solve the problem. We can worry about what it all means, later.
M*n = 360 ==> M = 360/n
x = 2*n
W*x = 480 ==> W = 480/x ==> 480/(2*n) = 240/n
W + M = 2500 ==> [240/n] + [360/n] = 2500
There is a single variable equation that is easily solved.
[240/n] + [360/n] = 2500
[24/n] + [36/n] = 250
24 + 36 = 250*n
60 = 250*n
6 = 25*n
n = 6/25
x = 2*n = 2*(6/25) = 12/25
W = 240/n = 240/(6/25) = 40*25 = 1000
M = 360/n = 360/(6/25) = 60*25 = 1500
Let's test everything.
W + M = 2500
1000 + 1500 = 2500 -- Check
x = 2*n
12/25 = 2*(6/25) = 12/25 -- Check
M*n = 360
1500*(6/25) = 6*60 = 360 -- Check
W*x = 480
1000*(12/25) = 12*40 = 480 -- Check
Features:
Rule #1 - Just name stuff. Name it all.
Rule #2 - Translate all relationships given in the problem statement. Get all of them. This may lead you to back up and define another variable or two.
Rule #3 (Which we didn't use this time) -- Is there anything else I should know about this situation. In a travel problem, for example, you are expected to know Distance = Rate * Time. In a rectangle problem, you are expected to know something about the perimeter or area or maybe the diagonals.
Rule #4 -- Let the notation help you. Once all the relationships are translated, just use the arithmetic to find the answers. You can worry about a relationship to the world later.
Rule #5 -- Don't be afraid to WRITE STUFF DOWN. The notation is much less likely to help you if you don't use it.
Rule #6 -- Do NOT memorize these rules. Find a systematic and useful methodology that makes sense to you.
Rule #7 -- Stay organized. See Rule #5. It's a whole lot easier to stay organized if you are not trying to cram the whole world inside your head.
Rule #8 -- Relax. Have a good time. Mathematics is your friend. Trust me on this!
