A question that ALWAYS stumps me.. someone help?

[taylor tay bags]

This is the only question i constantly stuff up in practice exams..

I can't get my head around it.. here's the question:

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 said it was B. y ≤ 2x, Purely because the question states; TWICE AS MANY RED WINES (x) THEN WHITE WINES.. so i said in text 'there 2 times as many red wines that are equal to or more than white wines.. the correct answer is E. someone tell me why?

[ReVeL]

This is a tough question, I remember doing it from a past paper. On first glance, both appear correct. The only way I could distinguish the two was by using an example. The sentance we're concerned with is:

This year he plans to make at least twice as many bottles of red wine as white wine. Where x = red wine and y = white wine.

So, lets say he makes 5 bottles of white wine, he would want to make at least 10 bottles of red wine. So we know the point (11,5) will be valid, and the point (9,5) will NOT.

Substitute the (9,5) point into B:
y ≤ 2x
5 ≤ 2(9)
5 ≤ 18
And here we have it. The answer for B says this point is valid when we know just using common sense without any maths that it's not.

Now, substitue the (9,5) point into E.
x ≥ 2y
9 ≥ 2 (5)
9 ≥ 10
Answer E says this point is not valid, which we know is correct.

Therefore, E is the correct answer. I'm sorry if this seems really confusing this was the best way I could remember how to do it before the exam. Maybe chuck it in your summary book.

Hope it helped.

[lolbox]

This is the only question i constantly stuff up in practice exams..

I can't get my head around it.. here's the question:

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 said it was B. y ≤ 2x, Purely because the question states; TWICE AS MANY RED WINES (x) THEN WHITE WINES.. so i said in text 'there 2 times as many red wines that are equal to or more than white wines.. the correct answer is E. someone tell me why?

Because x and y represent the number of wine bottles made, however many that may be. They later tell you that twice as many red wine bottles are made then white wine bottles, therefore x = number of red wine bottles, is double that of y. Thus x = 2y and the correct answer is x is greater then or equal to 2y (the inequality is greater then or equal to, and not less then or equal to, because he plans to make "atleast" twice as many bottles.

It is a pretty confusing q, and like the above post its probably best to make up some numbers and apply it to the question to determine which choice is correct.

[taylor tay bags]

This is a tough question, I remember doing it from a past paper. On first glance, both appear correct. The only way I could distinguish the two was by using an example. The sentance we're concerned with is:

This year he plans to make at least twice as many bottles of red wine as white wine. Where x = red wine and y = white wine.

So, lets say he makes 5 bottles of white wine, he would want to make at least 10 bottles of red wine. So we know the point (11,5) will be valid, and the point (9,5) will NOT.

Substitute the (9,5) point into B:
y ≤ 2x
5 ≤ 2(9)
5 ≤ 18
And here we have it. The answer for B says this point is valid when we know just using common sense without any maths that it's not.

Now, substitue the (9,5) point into E.
x ≥ 2y
9 ≥ 2 (5)
9 ≥ 10
Answer E says this point is not valid, which we know is correct.

Therefore, E is the correct answer. I'm sorry if this seems really confusing this was the best way I could remember how to do it before the exam. Maybe chuck it in your summary book.

Hope it helped.

Perfect. Thanks a lot. Life saver.

[lachymm]

Well explained, the way i think of it is, x must be 2 times greater than y therefore 1 x must = 2y's
Kinda how the last poster explained it