<p>this type of question always gets me confused of who is going to be multiplied by "something".
Ex:-</p>
<h2>a class of 29 students went to 2 trips: one to the zoo and one to the museum; every student attended at least one of the field trips, and 10 students attended both . IF TWICE AS MANY STUDENTS WENT TO THE ZOO AS WENT TO THE MUSEUM, how many students went to the zoo?</h2>
<p>-> now i said that { STUDENTS WENT TO THE MUSEUM = 2(STUDENTS WENT TO THE ZOO)}
so -> if we would resemble STUDENTS WENT TO THE ZOO to x+10 and<br>
then we would resemble STUDENTS WENT TO THE MUSEUM to 2x+20<br>
so-> (x-10)+(2x-10)+10= 29
then x=13 , which is the number of students who went to the zoo(3) + the number of students who went also to the museum (10)=13 Correct!</p>
<p>and 2x+10=26 , which is the number of students who went to the museum (16) + the number of students who went also to the zoo (10)=26 Correct!</p>
<p>and the number of students who went to the zoo only (3) + the number of students who went to the museum only (16) + the number of students who went to both the museum and Zoo(10) = 29. </p>
<p>so-----> clearly the the number of students who went to the zoo is (13).<br>
But for my bad luck the book says the answer is the opposite (26)! i hope i showed my problem enough and thanx</p>
<p>Total number = Number in group 1 + Number in group 2 - Number in both groups</p>
<p>In this case,</p>
<p>29 = 2x + x - 10</p>
<p>Because they tell us there are 29 kids in the class, total number = 29.
Because they tell us twice as many when on one trip as the other, I can make the number of people going on the trips be x and 2x.
They tell me 10 students attended both, so I also put that in that formula</p>
<p>Now, let me copy / paste the formula again. I haven’t changed anything.</p>
<p>29 = 2x + x - 10</p>
<p>Combine like terms,</p>
<p>29 = 3x - 10</p>
<p>Add 10 to both sides</p>
<p>39 = 3x</p>
<p>Divide by 3</p>
<p>x = 13</p>
<p>So, let’s refer back to the problem: x people went to the museum, 2x people went to the zoo. We found x to be 13, so 2x = 26 is the number of people who went to the zoo.</p>
<p>thanx guys too much for replying, but the answer isn’t the problem . i understand the question. what i need to know is " what do u do when u see if twice as many … as …?"
like when u see X is twice Y . so “is” is translated to “=” and “twice” to “'x2” , which mean<br>
x= 2xY. so i need a similar way to translate “if twice as many … as …”
and thanx again.</p>
<p>Your reasoning was mostly right, but you misunderstood the question. When you solved for x, you got the right number. However, if you look over the problem, the number of people that went to the zoo is TWICE the number who went to the museum. Thus, x was the number who went to the museum, and “twice the number” means 2x: the number of people who went to the zoo is the number of people who went to the museum doubled. You mentioned the idea of “X=2Y” and that is technically correct (where x would be zoo people and y would be museum), but it is not how you want to see this problem. You want to think it in terms of one variable (X), so that [number of people who went to the museum] + 2[number of people who went to the museum] equals 29. To get the zoo attendance, all you had to do was multiply the museum attendance by 2. Thus:
Assume:
Museum attendance = x
Zoo attendance = 2x</p>
<p>I think you have figured out your own mistake. It’s an easy slip to make. Here’s another old problem that is designed to trap kids who make that mistake:</p>
<p>If x = 2y and z is equal to the ratio of x to y, then z^2 =…</p>
<p>a) 1/4 b) 1/2 c) 2 d) 4 e) -1/2</p>
<p>If you are careful, this is easy algebra. If you make up numbers, its even easier.</p>
<p>In fact, going back to your original question: once you realized that there had to be 39 trips taken and twice as many of one kind as the other, you are better off skipping the algebra altogether and just PLAYING WITH NUMBERS! (I was about to say that I wish I had a dollar for every time that I gave that advice…) You need the numbers to add up to 39 and one has to be twice as big…just random trial and error won’t take that long before you find that 26 and 13 work. Or you could notice that if the ration has to be 2 to 1, then you are making three “piles” – so 39 divided by 3 gives you the size of the smaller pile.</p>