<li>145 300 610 1230
In the above sequence every term after the first is formed by multiplying by x and then adding y, where x and y are positive integers. What is the value of x + y?</li>
</ol>
<p>Does anyone know how to do this algebraically?</p>
<p>145x+y=300 (1)
300x+y=610 (2)
(2)-(1) and solve.</p>
<p>Thanks poof!!</p>
<p>Heres another Q regarding how to solve algebraically.</p>
<p>90n+23p = 4523
if n and p are positive integers in the equation above, what is one possible value of n+p.</p>
<p>How would you solve this ALGEBRAically?</p>
<p>You can't. There is an infinite amount of solutions.</p>
<p>i see.. im not very proficient with algebra =(, is there a general rule to when we are able to solve something algebraically or not? Solving questions algebraically is my weak point, i really want to get these questions off my chest for the oct test. Thanks alot bro!</p>
<p>^ Here's the general rule: If you have two variables, you need 2 equations to solve for them. If you have 3 variables, you need 3 equations. If you have 4 variables, you need 4 equations, and so on.</p>
<p>One variable: x + 5 = x^2 - 1 This can be solved using the quadratic formula.</p>
<p>Two variables:
x + 3y = 7
-x + y = 9</p>
<p>This can be solved by adding both equations to get 4y = 16. Then y = 4 and x = -5.</p>
<p>Three variables:
3x - 2y = z
x + z - 7y = 28
7x = 3z - y.
You can solve for x, y, and z as well.</p>
<p>So in this case, we need X AND y, so thus we need 2 equations. I get it! Thanks alot !</p>
<p>You would be wasting your time to approach this algebraically.</p>
<p>X can only be 1 or 2, and since 300-145=/=610-145, it has to be 2. Then, the fact that y=10 is apparent, and you get the answer of 12.</p>
<p>ANSWER to Quix inquiry: </p>
<p>Thanks poof!!</p>
<p>Heres another Q regarding how to solve algebraically.</p>
<p>90n+23p = 4523
if n and p are positive integers in the equation above, what is one possible value of n+p.</p>
<p>How would you solve this ALGEBRAically?</p>
<hr>
<p>METHOD 1:
if you stop and breathe for a second, you'll see a BIG hint in the question.
magic number is 23!</p>
<p>4523 and 23p.</p>
<p>if you say p=1.. and 4523-23p is 4523-23(1) = you get 4500.. which is divisible by 90. super simple. you get n=50 and p=1.. there fore answer n+p=51.</p>
<p>METHOD 2: this requires a calculator, which you can use on this section.
graph the equation. solve for p.
use your table function on your graphing calculator.
scroll down until you see a positive integer (whole number) in the y column.</p>
<p>you get these results</p>
<p>n p</p>
<p>4 181
...
27 91
...
50 1</p>
<p>so you add (n+p) =
all these are possible gridded answers
185, 118, and 51.</p>
<p>hope this helps!!!</p>
<p>300/145=x->2 y->10
610/300=x->2 y->10</p>
<p>So this pattern works.
x+y=>2+10=>12</p>
<p>Basic algebra and logic.</p>