How many hats for Mr Chan?

[Averagepunter]

Hats may be ordered from a supplier for $7.50 each or $60 for ten.
Mr Chan orders some hats and pays $2685 which includes $300 postage.
What is the maximum number of hats Mr Chan should receive?

 

[ksdhart2]

That sure is a very nice homework problem you've got there. But what are your thoughts? What have you tried? Please (re-)read the Read Before Posting thread that's stickied at the top of each subforum, and comply with the rules. Specifically, please share with us any and all work you've done on this problem, even including the parts you know for sure are wrong. Thank you.

Alternatively, assuming you're stuck at the very beginning and therefore have no work to show, consider: Is it cheaper to buy ten hats all at once or ten hats individually? Why? What does this suggest to you about the best course of action to maximize the number of hats Mr. Chan can afford?

 

[pka]

Hats may be ordered from a supplier for $7.50 each or $60 for ten.
Mr Chan orders some hats and pays $2685 which includes $300 postage.
What is the maximum number of hats Mr Chan should receive?

\(\displaystyle 2685-300=2385\)
\(\displaystyle \left\lfloor {\frac{{2385}}{{60}}} \right\rfloor =39\) that is the floor function.
\(\displaystyle 3285 \mod60=45\) and \(\displaystyle \frac{45}{7.5}=6\)

 

[Averagepunter]

Thanks for your prompt help.
Would you kindly explain in a simpler easy to understand way.

 

[ksdhart2]

Oh, sure, just give them the answer, why don't you?

 

[pka]

Thanks for your prompt help.
Would you kindly explain in a simpler easy to understand way.

Have a look at this calculation.
In that I gave you the answer. But unless you figure out what it means it is absolutely useless to you.

 

[MarkFL]

Hello, and welcome to FMH!

First, we want to remove the $300 postage to get the amount (in dollars) that went towards the hats, which is:

[MATH]2685-300=2385[/MATH]
Now, we want to divide this by 60, and remove the fractional part:

[MATH]\frac{2385}{60}=39.75\implies 39[/MATH]
This is what we get by using the floor function mention above. Okay, so:

[MATH]2385-39\cdot60=45[/MATH]
This is the amount we have left over to buy single hats at $7.50 per hat:

[MATH]\frac{45}{\dfrac{15}{2}}=2\cdot3=6[/MATH]
So, Mr. Chan could purchase 39 sets of 10 hats, or 390 hats, plus 6 individual hats, for a total of 396 hats.

 

[pka]

Hello, and welcome to FMH!
First, we want to remove the $300 postage to get the amount (in dollars) that went towards the hats, which is:
[MATH]2685-300=2385[/MATH]Now, we want to divide this by 60, and remove the fractional part:
[MATH]\frac{2385}{60}=39.75\implies 39[/MATH]This is what we get by using the floor function mention above. Okay, so:
[MATH]2385-39\cdot60=45[/MATH]This is the amount we have left over to buy single hats at $7.50 per hat:
[MATH]\frac{45}{\dfrac{15}{2}}=2\cdot3=6[/MATH]So, Mr. Chan could purchase 39 sets of 10 hats, or 390 hats, plus 6 individual hats, for a total of 396 hats.

In the futher, I hope that you don't scold me for jumping in to spoil you effort to get a student to try to work out the answer from hints.

 

[MarkFL]

In the futher, I hope that you don't scold me for jumping in to spoil you effort to get a student to try to work out the answer from hints.

Didn't you already provide the answer, and I just explained how to get that same answer differently? The OP may not have been exposed to floor functions and modular arithmetic yet. But, I didn't feel I was giving away anything not already provided, just explaining how to get there in a more elementary way.