Algebra word problem difficulty defining function

In summary, the conversation discusses the sales of cellphones at a price of $302 per unit, with 450 units sold in one week. It is also mentioned that for every one dollar increase in unit price, the weekly sales decrease by four units. The conversation then asks to form a function to describe the weekly sales income when the phone's price changes by X dollars, and if the store can sell cellphones at a price of $522. The attempted solution involves calculating the turnover as the product of price per unit and number of units sold, and determining the point at which no phones will sell based on the price increase. A more straightforward approach is suggested, which involves defining the number of sales
  • #1
late347
301
15

Homework Statement


cellphones are sold at price of 302$ per unit
In one week there were 450 units sold.

for every one dollar increase in unit price, the weekly sales of the phones fell by four units.
form a function which describes the weekly sales income when the phone's price changes by X dollars
Can the store sell cellphones at the price of 522 dollars?

Homework Equations


3. The Attempt at a Solution [/B]

I know that sales = turnover. But it does not seem to be the way to properly calculate this problem.

I had the wrong function evidently as my teacher sent me the correct solution to this problem. But I wonder if my original way is sensible or not.

I wonder if I should have somehow created a function which describes the weekly sales, from a zero units sold beginning. Like at the beginning hours of the business week, obviously nothing has been sold at that beginning hour. Past weekly sales would not matter in this sense, because new weekly sale is being calculated.

Normally of course turnover is the units sold times the price/unit.
Immediately it looks like at some point. The unit sale amount will become negative, when the price increases too high. Worst case for store is that nothing is sold = 0 unit sale amount.302 with no price change would equal 450 units
302+1 would make the change sales to 450 -4

304 would make sales to 450 - 4*2turnover = y

y = (price/ unit) x (unit amount sold)

y = ( 302 + x) * (450- 4x)

Can the store sell phones, at the unit price of 522?

522- 302 = 220

(302+220) * (450-4*220) = y

522 * ( 450 - 880) = y
522 * - 430 = y

-224460 = y

looks like nothing will be sold at that price,
This looks like it will be the case when one looks at the right hand side inside the brackets ( 450 - 4*220). This number should have been a positive number, for any amount of unit sales to have occured.
 
Physics news on Phys.org
  • #2
late347 said:

Homework Statement


cellphones are sold at price of 302$ per unit
In one week there were 450 units sold.

for every one dollar increase in unit price, the weekly sales of the phones fell by four units.
form a function which describes the weekly sales income when the phone's price changes by X dollars
Can the store sell cellphones at the price of 522 dollars?

Homework Equations


3. The Attempt at a Solution [/B]

I know that sales = turnover. But it does not seem to be the way to properly calculate this problem.

I had the wrong function evidently as my teacher sent me the correct solution to this problem. But I wonder if my original way is sensible or not.

I wonder if I should have somehow created a function which describes the weekly sales, from a zero units sold beginning. Like at the beginning hours of the business week, obviously nothing has been sold at that beginning hour. Past weekly sales would not matter in this sense, because new weekly sale is being calculated.

Normally of course turnover is the units sold times the price/unit.
Immediately it looks like at some point. The unit sale amount will become negative, when the price increases too high. Worst case for store is that nothing is sold = 0 unit sale amount.302 with no price change would equal 450 units
302+1 would make the change sales to 450 -4

304 would make sales to 450 - 4*2turnover = y

y = (price/ unit) x (unit amount sold)

y = ( 302 + x) * (450- 4x)

Can the store sell phones, at the unit price of 522?

522- 302 = 220

(302+220) * (450-4*220) = y

522 * ( 450 - 880) = y
522 * - 430 = y

-224460 = y

looks like nothing will be sold at that price,
This looks like it will be the case when one looks at the right hand side inside the brackets ( 450 - 4*220). This number should have been a positive number, for any amount of unit sales to have occured.
Another way to look at this problem is to define x as the number of dollars difference in the price of a single phone, above or below the base price of $302.
You know that the change in weekly sales is 4 phones less than the base sales of 450 phones for each dollar increase in the price.

Therefore, Number_of_Sales = 450 - 4 ⋅ x

Now, if no phones are sold, you set Number_of_Sales = 0 in the formula above, and obviously sales income will equal zero.

You can calculate the amount of price increase x beyond which no phones will sell. All that's left after that is to see if 302 + x < 522.
 
  • Like
Likes late347
  • #3
SteamKing said:
Another way to look at this problem is to define x as the number of dollars difference in the price of a single phone, above or below the base price of $302.
You know that the change in weekly sales is 4 phones less than the base sales of 450 phones for each dollar increase in the price.

Therefore, Number_of_Sales = 450 - 4 ⋅ x

Now, if no phones are sold, you set Number_of_Sales = 0 in the formula above, and obviously sales income will equal zero.

You can calculate the amount of price increase x beyond which no phones will sell. All that's left after that is to see if 302 + x < 522.
yes this is much more sensible way of going about the business of answering the problem... more straightforward.
I was thinking though...

The problem is easy to verify in a simple manner with calculator. Simply try and see, whether the new price causes the sales to plummet to 0 amount.

so the number of sales as a funcion of price increase would be thus. Am I correct in this previous statement <--- Sometimes I get confused which stuff is the function of something. Like the velocity as the function of time. If you say it that way, then I think velocity should be the Y axis, and time should be x values and in the horizontal axis. Then the graph would show how velocity increases or decreases with respect to time moving forward.

f(x) = 450- 4x
 
  • #4
late347 said:
yes this is much more sensible way of going about the business of answering the problem... more straightforward.
I was thinking though...

The problem is easy to verify in a simple manner with calculator. Simply try and see, whether the new price causes the sales to plummet to 0 amount.

so the number of sales as a funcion of price increase would be thus. Am I correct in this previous statement <--- Sometimes I get confused which stuff is the function of something. Like the velocity as the function of time. If you say it that way, then I think velocity should be the Y axis, and time should be x values and in the horizontal axis. Then the graph would show how velocity increases or decreases with respect to time moving forward.

f(x) = 450- 4x
For the function f(x) as described above, y = f(x) would represent the number of cell phones sold and x would represent the increase or decrease in the price of each phone from the original $302 per phone.

When there is no price increase, x = 0 and f(0) = 450 phones, which agrees with the problem statement.

When the price increases, x will be a positive number and f(x) will decrease from 450 phones; when the price decreases, x will be negative and f(x) will increase beyond 450 phones, at the rate of 4 phones up or down depending on whether the price decreases or increases, respectively.

In order to find the amount of increase in the price of the phone which results in zero sales, the x-intercept of f(x) will give you that amount.
 
  • #5
SteamKing said:
For the function f(x) as described above, y = f(x) would represent the number of cell phones sold and x would represent the increase or decrease in the price of each phone from the original $302 per phone.

When there is no price increase, x = 0 and f(0) = 450 phones, which agrees with the problem statement.

When the price increases, x will be a positive number and f(x) will decrease from 450 phones; when the price decreases, x will be negative and f(x) will increase beyond 450 phones, at the rate of 4 phones up or down depending on whether the price decreases or increases, respectively.

In order to find the amount of increase in the price of the phone which results in zero sales, the x-intercept of f(x) will give you that amount.
I was wondering about one thing...

Did i actually arrive at the correct result even though I approached the problem through the turnover function instead of the amount of cellphones function?

If my original function is set as an equation such that

0= (302+x)(450-4x)

X either 112.5
Or

X -302 (as I recall)

I suppose the positive solution would be more appropriate.

Although one might say that " I will increase the price by a negative amount"
It would be silly way of saying that in a business setting.

Probably it looks like 112.5 dollars is the maximum price increase and with that price increase there will be no products sold at all.

Of course in real life if the unit cost of something would be 0 dollars per flat-screen tv...

There would be many customers... but no sustainable business for the store itself it seems.
 
  • #6
late347 said:
I was wondering about one thing...

Did i actually arrive at the correct result even though I approached the problem through the turnover function instead of the amount of cellphones function?

If my original function is set as an equation such that

0= (302+x)(450-4x)

X either 112.5
Or

X -302 (as I recall)

I suppose the positive solution would be more appropriate.

Although one might say that " I will increase the price by a negative amount"
It would be silly way of saying that in a business setting.
You don't see it much currently, but increasing the price of something by a negative amount is also known as a "price cut", and price cuts have been known to increase sales so that a company makes more total revenue although the unit price is less. For example, computers were once so expensive that only governments and big business could afford them. Newer technology allowed smaller and cheaper computers to be made, and eventually individuals could own a computer. Even after that occurred, prices continued to decline, and more computers were sold.
Probably it looks like 112.5 dollars is the maximum price increase and with that price increase there will be no products sold at all.

Of course in real life if the unit cost of something would be 0 dollars per flat-screen tv...

There would be many customers... but no sustainable business for the store itself it seems.

It's always hard to make money by giving away free stuff.
 

Related to Algebra word problem difficulty defining function

What is an algebra word problem?

An algebra word problem is a type of mathematical problem that involves using symbols and equations to represent and solve a real-life situation. These problems often require critical thinking and problem-solving skills.

What makes defining functions difficult in algebra word problems?

Defining functions in algebra word problems can be difficult because it requires understanding how different variables and quantities are related to each other, as well as understanding how to represent these relationships using mathematical equations and symbols.

What strategies can be used to improve difficulty in defining functions?

One strategy to improve difficulty in defining functions is to practice solving various types of algebra word problems and becoming familiar with different problem-solving techniques. Another helpful strategy is to break down the problem into smaller, more manageable parts.

How can I identify the function in an algebra word problem?

To identify the function in an algebra word problem, look for key words that indicate a relationship between two quantities, such as "increases by," "decreases by," or "equals." You can also look for patterns in the given information, such as a constant rate of change.

Why is it important to understand functions in algebra word problems?

Understanding functions in algebra word problems is important because it allows you to solve real-world problems and make predictions based on mathematical relationships. It also helps develop critical thinking skills and lays a foundation for more advanced math concepts.

Similar threads

  • General Math
Replies
1
Views
1K
  • General Math
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
4K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • General Math
Replies
2
Views
6K
  • Calculus and Beyond Homework Help
Replies
1
Views
5K
  • Precalculus Mathematics Homework Help
Replies
3
Views
17K
  • General Discussion
Replies
5
Views
5K
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
7K
Back
Top