math questions....

Test Preparation SAT Preparation
1

<p>i dont know whats wrong with me i keep forgetting the most basic concepts eg :</p>

<p>A restaurant has 19 tables that can seat a total of 84 people. some tables seat 4 and others seat 5 people. how many tables seat 5 people?---i will not provide the answer choices becuz i need an algebraic method-NOT plugging in!- i no weird but i really need to understand the concept</p>

<p>The other question:</p>

<p>a four digit integer, WXYZ, in which X, Y Z and W each represent different integers and is formed according to the following rules:
1. X= W + Y + Z
2. W= Y + 1
3. Z= W-1
can any1 plz explain?</p>

2

<p>A+B=19
4A+5B=84</p>

<p>You want to know B, so solve for A.</p>

<p>A=19-B
4(19-B)+5B=84
76-4B+5B=84
B=8</p>

<p>What you need to know: substitution</p>

3

<p>Since W is in all of them, it is simple to solve for it.</p>

<p>X=W+(W-1)+(W+1)
X=3W</p>

4

<p>thannx i get it now somehow im becomin more and more stupid as the exam is approaching from 800 to 670s!!! :(</p>

5

<p>heres another question that i cant get!
t^2-k^2<6
t+k>4
if t an k are positive integers wat is the value of t?</p>

<p>can anyone plz explain the solution for this (the answer is 3 btw)
wat i came up with was:
t+k=4
k=4-t
t^2-(4-t)(4-t)<6
etc. but here i was wondering whether the minus sign before the quadratic changes the signs of the quadratic equation plz clarify
thnx in advance</p>

6

<p>im sure there is a better approach to this problem, but this was my way...</p>

<p>since t and k are positive integers, the only way t^2-k^2 can be less than 6 would be when t and k are 1,2,3, or 4. </p>

<p>ex. if t was 5 and k was 4... t^2-K^2 = 7
ex. #2 if t was 6 and k was 5 t^2-K^2 = 11</p>

<p>so the only way t^2-K^2 < 6 would be when t and k are between 1-4</p>

<p>t+k>4 so the only possible combination would be (1,4), (2,3), or (3,4)</p>

<p>(1,4) and (3,4) doesnt work because it does not agree with t^2-k^2<6</p>

<p>(2,3) works. </p>

<p>the only problem with my way is that t and k could equal 2 or 3.</p>

7

<p>Is there more info for this problem? There is more than one solution...</p>

<p>E.g.:</p>

<p>t = 1, k = 5
t = 2, k = 5
t = 3, k = 5</p>

<p>and in fact any integers t and k with t < k and t + k > 4 are all solutions...</p>

8

<p>I'd just quickly factor it out and then use logic. So (t-k)(t+k) > 6. Fastest there is to quickly try each one, either mentally if you can or with a calculator.</p>

<p>The WXYZ problem doesn't work... It says they are different integers, yet Z = Y.</p>

9

<p>for the wxyz problem i just plugged in numbers until i got one that worked. i started off with x being like 8,9 or some other high number because X= W + Y + Z, oddly enough this way of working the problem actually got me the right answer in two to three minutes.</p>

10

<p>Two to three minutes?
You need to be knocking off problems in under a minute each!</p>