Inequality sign

[lacoste]

Question 6
Russell is a wine producer. He makes both red and white wine.
Let x represent the number of bottles of red wine he makes and y represent the number of bottles of white wine
he makes.
This year he plans to make at least twice as many bottles of red wine as white wine.
An inequality representing this situation is
A. y ≤ x + 2
B. y ≤ 2x
C. y ≥ 2x
D. x ≤ 2y
E. x ≥ 2y



I don't get how they got the answer.

What is your answer and explain?

[cobby]

Is the answer b?
If he plans to make twice as many bottles of red than white, that would give y=2x
Because the question says 'at least' then he could make more than double the amount of white wine.

Hence y ≤ 2x

[lacoste]

answer is E.

i would have chose the same as you cobby

[Gloamglozer]

Are you sure the answer is E?  I would have said B as well.  Maybe the answer is wrong?  Where did you get the question from?

[jackinthepatch]

I got E...

x = red wine
y = white wine

He wants to make twice as much red wine than white, which gives x = 2y. But to make at LEAST twice the amount of red wine it should be x ≥ 2y

Actually...B and E are both right I reckon...

[doboman]

Question 6
Russell is a wine producer. He makes both red and white wine.
Let x represent the number of bottles of red wine he makes and y represent the number of bottles of white wine
he makes.
This year he plans to make at least twice as many bottles of red wine as white wine.
An inequality representing this situation is
A. y ≤ x + 2
B. y ≤ 2x
C. y ≥ 2x
D. x ≤ 2y
E. x ≥ 2y

Hey Lacoste, I'll give it my best shot at explaining- but I really hate these types of questions. This is the most important line of the whole stimulus: This year he plans to make at least twice as many bottles of red wine as white wine. What it's saying is; for every one bottle of white wine, there is to be 2 or more bottles of red wine. Now; this is how i used to do it. X is our variable, so muck around with it. As it says, for every 2 X, there's 1 Y, divide all the X's by 2. You will end with, .5X = Y. Therefore, all you need to do now is put in the equality sign. So, .5X is ≥  Y. Which is the same as, x ≥ 2y. I hope that made sense.

[ReVeL]

I remember doing this exam(2007 was it?), and this was the 1 question I got wrong. At first glance, most people would say B but yes, the answer is actually E. Here is proof.

So, "he plans to make at least twice as many bottles of red wine as white wine". To make things easier, I find it helpful to put the problem in context. If he makes 5 bottles of white, Russell must make atleast 10 bottles of red. Subsituting x=10 and y=5 into both B and E satisfies both contraints, telling us nothing. But, we can subsitute something we know to be incorrect to find the answer.

Let y=5 and x=6. We know this does NOT satisfy the constraint, and so if either B or E does satisfy it, we know that answer will be incorrect.

B first:
y ≤ 2x. Subsitute y=5, x=6.
5 ≤
5 ≤ 12.

This contraint is therefore WRONG, because even though 12 is greater or equal to 5, we KNOW that if he makes 5 bottles of white, he must make atleast 10 bottles of red.

Now lets subsitute into E:
x ≥ 2y. Subsitute y=5, x=6.
6 ≥
6 ≥ 12.

This shows E to be correct, because 6 is NOT greater or equal to 12, hence this constraint is showing that if he makes 5 bottles of white, he cannot make 6 bottles of red because this does not comply with the statement "he plans to make at least twice as many bottles of red wine as white wine".

Tough question guys, it requires quite abit of thinking and the majority of people will get this incorrect. If you can master solving these it will greatly help you come the end of the year. Hopefully I explained it decently.

[plato]

I got E...

x = red wine
y = white wine

He wants to make twice as much red wine than white, which gives x = 2y. But to make at LEAST twice the amount of red wine it should be x ≥ 2y

Actually...B and E are both right I reckon...

B and E cannot both be correct
E says x ≥ 2y which is the correct answer to this question.
B says y ≤ 2x  which can also be written as 2x ≥ y

Since 2x ≥ y  is not the same as   x ≥ 2y , B is not equal to E