<p>A jar contained red and green marbles in a ratio of 3 to 4. After 6 red marbles were added to the jar, the ratio became 3 to 2. How many green marbles did the jar then contain?</p>
<p>(I made up some weird logic in my head that makes no sense, and basically guessed the answer. Does anyone have an actual way to do this? thanks)</p>
<p>it's easy .
First the ratio was 3 to 4 , so let's say there were 3x red and 4x green.
Then the ratio became 3 to 2 , so there were 3y red and 2y green.
We added 6 red marbles , so :
3x + 6 = 3y (1)
3x + 4x + 6 = 3y + 2y
7x+6 = 5y (2)
Subtract 1 from 2
4x = 2y or better say y = 2x. let's subtract this in 1
3x + 6 = 3 * 2x=6x
3x = 6 x= 2 y = 4 . at the end there were 2y green marbles 2y=2*4=8</p>
<p>Also, if R is the number of red marbles initially and G is the number of green marbles initially,</p>
<p>G = 4/3 R
G = 2/3 (R + 6)
4/3 R = 2/3 (R + 6)
4/3 R = 2/3 R + 4
2/3 R = 4
R = 6
G = 4/3 R
G = 8.</p>
<p>Another way:
From the problem:
First ratio is 3/4 --> x/y = 3/4
Second ratio is 3/2 --> (x+6)/y = 3/2</p>
<p>Change (x+6)/y --> x/y + 6/y and substitute 3/4 for x/y.</p>
<p>--> 3/4 + 6/y = 3/2</p>
<p>Then you get y = 8, and x follows from that.</p>
<p>Jennifer: It really depends on the problem and your mathematical ability. Most of the time, I end up using real numbers instead of variables because real numbers make more sense.
For the above problem for example, if it were multiple choice, I could easily test the answer choices because I'm good with mental arithmetic. Most people would just do it algebraically. Have you found your strengths yet? You should and use them on the SAT. Develop your own style.</p>
<p>CULD SUMBUDY HELP ME OUT WITH THIS PROBLEM???</p>
<p>A researcher found that the higher the temperature of a room, the lower the average positive outlook rating of the people in the room. If t is the temperature of the room and p(t) is the average positive outlook rating, which of the following could express this function?
a.p(t)=t/5
b.p(t)=t-5
c.p(t)=5(t^3)
d.p(t)=5sqrtt
e.p(t)=5^-t</p>
<p>I guess, it's choice E. Look, if t is higher, then p is lower. So let's substitute real number for t, and find what p is. And again let's try bigger t this time, and according to what's been told, p should be less than the previous p.
before using this method, we should eliminate some choices that clearly don't follow the rule.
for A, it can't be the choice. because, it is, the higher t is, the higher p is. can you see it?
for B, it's same as A. the more t is, then the more p is.
for C, doesn't it look same to you? try substituting some easy numbers.
for D, wow same again!!!
we have eliminated every wrong choice. so the answer is E.
let's check if it's true or not.
if t=0, then p=1.
if t=1, then p=1/5=0.2
if t=2, then p=1/25
see? is my explanation understandable for you?</p>
<p>Okay, so if temperature is going up, positive outlook is going down. So draw the graphs and figure out the one where as temperature goes up, positive outlook goes down. The answer is E.</p>
<p>It's really quite simple!</p>
<p>Yup I totally get it now.</p>
<p>Thnx</p>
<p>that's good then</p>
<p>k here's what i thought would be an easy one.. but then couldn't figure it out :(</p>
<p>On her test, Cathy answered 5/6 of the questions correctly. If Cathy answered 18 of the first 27 questions correctly, then the total number of questions on the test must be at least:
(a) 32
(b) 36
(c) 45
(d) 48
(e) 54</p>
<p>DuckTape14, I made a post where I answered your question and gave you an explanation, but I decided that I want YOU to figure out the answer. I'll give hints. Please, everyone, don't shout out the answer! </p>
<p>It may take a while, but I think it will be more valuable if you figure it out.</p>
<p>Hint: Cathy answered exactly 5/6 of the questions correctly. And of course, the number of questions she answered correctly has to be a whole number. So, there can't be 29 questions on the test, because 5/6 of 29 questions is not a whole number.</p>
<p>So, what answer choices can we eliminate first?</p>
<p> I think we need to start a new thread </p>
<p>Try to set up an equation and understand.</p>
<p>Try not to guess and check, or you'll probably end up G&C'ing more of the test than time will allow.</p>
<p>^ err.. guessing and checking can sometimes work </p>
<p>blddrake44, sometimes guess and check will be faster than trying to set up an equation. </p>
<p>aisgzdavinci, I don't see any need to start a new thread. I actually like having all the math questions on one big thread.</p>
<p>mm..</p>
<p>I meant my message more towards anyone who would try to guess and check the whole test with his or her calc. I tutored math a little at my school, and there are more people who try to do it than I thought.</p>
<p>They tell me they run out of time.</p>
<p>Well, you usually don't have to guess and check the whole test. I guess which ever way is faster for you, that would be the way to go.</p>
<p>The problem can be solved in this manner:</p>
<p>18 + x / 27 + x = 5 / 6</p>
<p>5(27 + x) = 6(18 + x)
135 + 5x = 108 + 6x
27 + 5x = 6x
27 = x</p>
<p>Now, to get the number of total questions you add the value of x to the denominator because that was the total number of questions:</p>
<p>27 + 27 = 54</p>
<p>The answer is 54</p>
<p>okay, you're not supposed to answer the question for him. You should let him answer the question on his own, while giving some hints.</p>
<p>Oh well... too late.</p>
<p>Okay, here's the explanation that I saved on my computer. I was going to wait until DuckTape figured it out and then give the whole explanation.</p>
<p>Okay, so Cathy answered 18 out of 27 correctly. That means that she had to answer a lot of questions right after the first 27 in order to get 5/6 of the questions correctly.</p>
<p>Let x be the number of questions after the first 27. Then x+18 is the greatest possible number of questions Cathy can get right (if she answers all x questions correctly). Then x+27 is the total number of questions on the test. That means that</p>
<p>(x+18)/(x+27) = 5/6</p>
<p>Solving for x, you get x = 27.</p>
<p>So there were 27 + 27 = 54 total questions on the test, at least.</p>
<p>Another way to think of it: </p>
<p>Well, first if Cathy answered exactly 5/6 of the questions correctly, the answer can't be A or C, because 5/6 of choices A and C would not give you a whole number.</p>
<p>Let's look at B, 36. That means Cathy answered 30 correctly. But if she answered 18 of the first 27 questions correctly, no matter how many she answers correctly after that, the most she can get is 27 correct (because she can get all of the last 9 questions correct). So the answer's not B.</p>
<p>The same goes with D. She'd have to answer 40/48 correctly in order to get 5/6 correct, but the most she can get is 39 (that is, if she answers the last 21 questions correctly).</p>
<p>The last choice is E, 54. Cathy would have to answer 45 correctly, which she can do if she answers the last 27 questions correctly.</p>
<p>The correct answer is E.</p>