<p>A four digit integer, WXYZ in which w x y and each represent a different digit is formed according to the following rules.</p>
<ol>
<li>x = w+y+z</li>
<li>W=y+1</li>
<li>Z = w-5</li>
</ol>
<p>What is the four digit integer</p>
<p>Is the answer 5940 ?</p>
<p>Since X has to be a single digit number, you want to minimize the values of the other 3 digits, so that when you add them up the sum doesn’t exceed 9. Now, what is the minimum single-digit number that can be Z (which looks to be the easiest starting point)? 0. Therefore, since Z = W-5, 0 = W-5, so W = 5. If W = 5, then Y = 5-1 = 4. X = 5+4+0 = 9, so the number is 5940.</p>
<p>Yea the answer is 5940, thanks for the amazing explanation. If you could explain this question as well it would be really helpful:</p>
<p>n(t)= t^2/2 -20t +k</p>
<p>There was a 100 day period when the number of bees in a certain hive could be modeled by the function n above. in the function k is a constant and n(t) represents the number of bees on a day number t for 0 less than or equal to t which is less than or equal to 99. on what number day was the number of bees in the hive the same as it was on day number 10?</p>
<p>Alright…</p>
<p>Start off by plugging in 10 for t in the function. By simple arithmetic, you will arrive at the function n(t) = -150 + k. Now, you know that t = 10 gives you -150 + k (but k is a constant, so you can ignore it). Therefore, you are looking for another value of t that when plugged in will net you -150 + k.
Hence, you can set up the equation:
(t^2 / 2) - 20t = -150 (if you don’t get why you can do this, I’ll elaborate)
which, after basic algebraic solving, will become:
t^2 - 40t + 300 = 0, which can be factored into:
(t - 30) x (t - 10) = 0.
Thus, the answer is day 30 (note that t can be either 10 or 30 in the factored equation above; this shows that either value for t will net you the same result; this is why the number of bees on day 30 = the number of bees on day 10).</p>
<p>p.s. it’s probably easier to just plug in answers, assuming they’re available.</p>
<p>Thanks, what are those types of questions called? I need to practice them, would it be under functions?</p>
<p>These problems do have a distinctive and are easily characterized (a paragraph of text, a function of some sort, a bit of data), so you should be able to recognize them fairly easily when looking for practice. But the general category to place these under is most likely ‘functions’.</p>
<p>Functions will either be solved using 3 ways according to cases
1)either substitute values
2)Set values in function and solve for constants(in case of level 5 problem,but they are really easy once u get to do some problems of them).
3)Functions that has graph you can solve this by f(x) = y; or that will be translated to f(x) = y = will be plotted on graph like this (x,y).</p>
<p>I used to have problems in functions,but after solving many exams they are pretty easy just takes more time to solve them.</p>