You know the drill by now. The prize this week will, once again, be beta access to the Math Guide, which is really coming along nicely, if I do say so myself. I kinda can’t believe it’s going to top 300 pages, but at this rate we’re definitely heading in that direction.
A stereo equipment store owner notices that all his customers spend between $110 and $298, inclusive, in his store when they come in. For no discernible reason other than that I need a difficult math problem, he decides to express the range of dollar amounts his customers spend, s, in an inequality of the form |s – j| ≤ k, where j and k are constants. What is jk?
Questions like this aren’t super common on the SAT, but when they appear they always follow the same pattern:
In this case, the range is 110 < s < 298, so the middle of the range is (110 + 298)/2 = 204 , and the distance from the middle to the ends of the range is (298 – 110)/2 = 94.
So j = 204, and k = 94. Their product is 19176.
For more practice with this kind of question, go here.
J is 204. K is 94.
So the answer, jk, is 19176.
Nice work. Welcome to the Beta! (Log into docs.google.com with the email you provided to see the document.)
However, I only got the answer because I remembered the equation from your book. How would we do it without the formula?
Start by setting up the inequality range: 110 < s < 298, and then try to subtract something from s that will create the same number on both sides (with opposite signs, of course). Basically, trial and error.