Question 473848: one number is 17 greater than a second number. when the lesser number is subtracted from twice the greater number, the difference is 79.
Let x=the greater number.write an expression for the smaller number.
please help tutor! :)
Answer by karaoz(32)   (Show Source):
You can put this solution on YOUR website!
If they dare to use x to denote the greater number than we should be polite enough to use something else for the smaller number. How about s (should remind us of the word "smaller")? So, x = the greater number and s = smaller number. Let's now translate the problem statement but using x instead of "the greater number" and s instead of "the smaller number".
Original problem statements / Translation
"One number is 17 greater than a second number."
"x is 17 greater than s."
(if "one" number is greater than a "second" number, then we cannot afford such a level of stupidity not to figure out that "one" number is x and "second" number is s).
"When the lesser number is subtracted from twice the greater number, the difference is 79."
"When s is subtracted from 2x, the difference is 79."
"Let x = the greater number."
"Let x = x."
"Write an expression for the smaller number."
"Write an expression for s."
Let's sort this out now. First of all, the last sentence is telling us that what they want is to find an expression for s. The assumption is that they want a simple algebraic expression since the problem statement is already one way of expressing s (although a quite cumbersome way).
From the first sentence we have:
x = s + 17, which means that
s = x - 17.
Right, so we are done! We already have an expression for s.
But let's humor the author of the question and see what the other sentences have to offer.
From the second sentence we have:
2x - s = 79, which means that
s = 2x - 79.
Strangely, we found yet another expression for s and that is all we have since the third sentence is rather irrelevant. But if both of these expressions are true (as stipulated by the problem statement) then it means that:
s = x - 17 and also
s = 2x - 79.
If both of these are true then
x - 17 = 2x - 79, which means that
x = 79 - 17 = 62.
Well, well, x is not just any great number. It must be 62 if both of the first two sentences are true. But if x = 62 then our little s must be 45 (we can figure this out from any of the first two sentences knowing that x = 62).
So, one expression for s is:
s = x - 17.
Another expression for s is:
s = 2x - 79.
And since both of these must be true then this poor little s is not as free as we may have imagined. Instead, it is rather fixed and it is equal to 45.
A very degrading expression for apparently rather free letter s is then simply:
s = 45.
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