Graphs and Relations turning words into inequality??

[jedcarey17]

Hey guys,

Can someone please help me with turning written information into linear inequalities. The questions that ask, for example:
2012 Exam 1 Module 3 Question 8:
Let w be the number of loaves of white bread that are made each day
Let b be the number of loaves of brown bread that are made each day

At least five loaves of white bread will be made for every loaf of brown bread that is made.
Write the inequality that could be written to represent this constraint.


I can never wrap my head around them.

Cheers

[keltingmeith]

First, don't even think about the inequality - get the constants in first. So, every time we make ONE b, we also make FIVE ws.

So, we have b ? 5w

Now, we need to figure out the inequality. It says we have AT LEAST 5ws for every b, so we could have more ws. So, let's consider a case with more - maybe we make 6 ws. We must make 1 b, so we have:

5w ? b
11w ? 2b

Dividing the second equation by 2, we have:

5.5w ? b

So, this means that the amount of w must be greater than or equal to b (if we assume 5w=b), as we can see that an expression that logically held true, came down to more ws than bs. So, our inequality is 5w >= b

[Splash-Tackle-Flail]

Correct me if I'm wrong, but I got w>=5b. First I drew up a table, that shows when he makes one brown bread he makes at least 5 white bread, so then if theres one brown bread for every five white bread, then to find the number of white bread made, you would have to multiply the number of brown bread made by 5 (i.e. if there are 2 brown bread made, then he would make at least 10 white bread because 2*5=10). This gives w=5b.

Now the question says he makes at least five loaves of white bread, so he could make more than 5 and still satisfy the inequality. THerefore 'w' can be greater than '5b'.

This gives w>=5b.

[jedcarey17]

Thanks for the reply but the answer is w>=5b according to the answers. I asked a friend and they showed me that as they make 5 w's for every b it can be shown like this:

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|
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|     |
w    b

So w=5b,

And because there's at least 5w's for 1b then, w>=5b
The direction of the sign I'm not 100% convinced in my head that it always points to the number but for every example I've done it points to the side with the number.

Thanks though!

[keltingmeith]

Whoops - my bad! Thanks for catching me, Splash-Tackle-Flail.