minimum number of...

eddy2017

eddy2017

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Oct 27, 2017
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Hi, dearest teachers, professors and Math buffs:
A friend of mine sent me this problem. I asked him if he was sure this was the real problem. He said he copied it from someone else. I was not going to post it, because I do not understand why the t-shirts have two different prices. But I am curious. Caveat: According to him the wording is just fine. For what is worth, here it is:

The school drama club is planning to sell t-shirts at a musical production. The cost of the t-shirts is a one-time screening fee of $150 plus $6 per t-shirt ordered. Club members plan to sell each shirt for $15 dollars. What is the minimum number of t-shirts they need to sell in order to make a profit of $900 dollars?
Given
cost of the t-shirt =150 dollars fir a screening fee plus 6 dollars if a shirt is ordered.
club members want to sell each shirt for 15 dollars.
Thanks for your help!
eddy
 
Eddy

The shirts do not have two different prices. They have two different components of cost. The cost is

[MATH]150 + 6n, \text { where } n \text { is the number of shirts purchased.}[/MATH]
I could go into a lot of economic detail about the difference between unit cost and selling price per unit, but that is not in fact necessary. All that is necessary is to recognize that the overall cost is dependent on the number of shirts ordered. Remember what the Khan of Khan says:

The first step is to understand the problem.
 
JeffM said:
Eddy

The shirts do not have two different prices. They have two different components of cost. The cost is

[MATH]150 + 6n, \text { where } n \text { is the number of shirts purchased.}[/MATH]
I could go into a lot of economic detail about the difference between unit cost and selling price per unit, but that is not in fact necessary. All that is necessary is to recognize that the overall cost is dependent on the number of shirts ordered. Remember what the Khan of Khan says:

The first step is to understand the problem.
Click to expand...
Thanks for replying Mr J.
But if no shirt has been purchased?. Any hint about finding the value of n?.
 
Eddy

One of the two major types of problem addressed by algebra is finding what number or numbers satisfy certain conditions. What is the only condition specified in this problem?

What does that condition mean in practical terms? Algebra is actually used to solve practical problems in day-to-day life. I am not sure how old you are, but this is a type of problem that comes up all the time in running business.
 
eddy2017 said:
total of t-shirts to sell to make a profit of $900 ?
tts=?
tts(total t-shirts to be sold) = $150 + 6n
perhaps?
150 + 6n ( n standing for t-shirts in this case)
but how to find n?.
Click to expand...
 
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JeffM said:
Eddy

One of the two major types of problem addressed by algebra is finding what number or numbers satisfy certain conditions. What is the only condition specified in this problem?

What does that condition mean in practical terms? Algebra is actually used to solve practical problems in day-to-day life. I am not sure how old you are, but this is a type of problem that comes up all the time in running business.

The condition specified in this problem is the minimum of shirts that the club needs to sell to make 900 dollars.
Click to expand...
 
eddy2017 said:
Thanks for replying Mr J.
But if no shirt has been purchased?. Any hint about finding the value of n?.
Click to expand...
Try this:
You have classmates who like pepsi and don't mind paying $2 a can. You can take an Uber to a store for $3 and buy pepsi for $1 a can. How many orders do you need to make a profit of $5?
 
lev888 said:
Try this:
You have classmates who like pepsi and don't mind paying $2 a can. You can take an Uber to a store for $3 and buy pepsi for $1 a can. How many orders do you need to make a profit of $5?
Click to expand...
It depends on the amount of classmates that want Pepsi
How can I know without knowing how many people I'm going to sell it to?
 
eddy2017 said:
It depends on the amount of classmates that want Pepsi
How can I know without knowing how many people I'm going to sell it to?
Click to expand...
That's the question. You want to make a profit of $5. How many orders will it take?
 
I will help by almost solving lev888's problem.

You want to make $5 and pay $3 for an Uber. So you need to make back $8 in total. Now you make a profit of $1 per can of soda you sell. So how can's do you need to sell?
 
eddy2017 said:
It depends on the amount of classmates that want Pepsi
How can I know without knowing how many people I'm going to sell it to?
Click to expand...
Exactly! That is why lev888 asked how many cans must you sell to make a profit of exactly $5.

If you sell 0 cans then you make $0. However if you sell a million cans you make serious money. $5 is somewhere in the middle there! So how many cans must you sell to profit $5 is a reasonable question to ask.
 
Think I have it
8 orders of pepsi.
8 cans *2 =16
-3 (taxi ride)
13-8 (that I shelled out for the 8 pepsis I bought)= 5 dollars profit.
 
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eddy2017 said:
Think I have it
8 orders of pepsi.
8 cans *2 =16
-3 (taxi ride)
13-8 (that I shelled out for the 8 pepsis I bought)= 5 dollars profit.
Click to expand...
Ok, good guess.
Can you solve it algebraically? Set up an equation with the number of orders as the unknown and solve it.
Hint: the question is about profit - can you write the expression for profit that includes the number of orders and then equate it to 5?
 
lev888 said:
Ok, good guess.
Can you solve it algebraically? Set up an equation with the number of orders as the unknown and solve it.
Hint: the question is about profit - can you write the expression for profit that includes the number of orders and then equate it to 5?
Click to expand...
8(2)-3-8= 5
 
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