SOLUTION: So hi, (: I have two problems that I keep getting wrong ? Heres the first one.. A toy company spends $1500 each day for factory expenses plus $8 per teddy bear. If the compa

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Question 415235: So hi, (:
I have two problems that I keep getting wrong ?
Heres the first one..
A toy company spends $1500 each day for factory expenses plus $8 per teddy bear. If the company sells the bear for $12.00 each, how many bears must it sell in on day to equal it's daily cost?
I did the problem & put this:
1500/12=125
So 125 bears have to be sold to equal the daily cost.

I have to define a variable for the unknown that you are looking for and then write an equation you can solve for that variable,
So yeah I'm confused
Anyways, Here's the 2nd problem:
Solve the following problem. Include your work by showing steps you took to solve it or explain in words what you did.
If consecutive integers are defined as n, n+1, etc., How would consecutive EVEN integers be defined?
Problem: The sum of four consecutive even integers is 308. Write & solve an equation to find the four integers.
Thanks guys, your all very helpful! Hope someone see's or understands this fast :)

Found 2 solutions by Theo, solver91311:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Problem Number 1:

A toy company spends $1500 each day for factory expenses plus $8 per teddy bear. If the company sells the bear for $12.00 each, how many bears must it sell in on day to equal it's daily cost?

x = number of teddy bears sold per day.

x * 12 = revenue from teddy bears per day.

cost to build x teddy bears is equal to 1500 + 8*x

The revenue must equal the cost to break even.

revenue = 12*x
cost = 1500 + 8*x

Set them equal to each other to get:

12*x = 1500 + 8*x

subtract 8*x from both sides of the equation to get:

4*x = 1500

divide both sides of the equation by 4 to get:

x = 375.

They have to sell 375 teddy bears each day in order to break even.

their revenue will be 12 * 375 = 4500

Problem Number 2:

Solve the following problem. Include your work by showing steps you took to solve it or explain in words what you did.
If consecutive integers are defined as n, n+1, etc., How would consecutive EVEN integers be defined?
Problem: The sum of four consecutive even integers is 308. Write & solve an equation to find the four integers.

Consecutive even numbers would be n, n+2, n+4, etc.

n + n + 2 + n + 4 + n + 6 = 308

combine like terms to get 4n + 12 = 308

subtract 12 from both sides of the equation to get 4n = 296

divide both sides of the equation by 4 to get n = 74

the numbers are:

74 + 76 + 78 + 80 = 308

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the number of items produced in one day. Then dollars is the variable cost based on the number of items produced and must be the total cost. The total revenue is the price times the number of items sold. So if you let be the number of items sold, then dollars is the revenue.

The difficulty with the problem as stated is that there is no data or information given that allows us to relate the number of items produced with the number of items sold.

The breakeven point is where the total revenue is equal to the total cost:

.

Which is a single linear equation in two variables, having an infinite number of solutions. This means there is no definative answer to the question.

If you assume, though you really have no right to do so given the wording of the problem, that the number sold is equal to the number produced, then you have two equations:

and

And you can solve the system by first substituting:

and then solving by ordinary means.

However, consider the case where they sold 100 items less than they produced. Then you would have:

and

And you can solve the system by first substituting:

and the solution in this case is very different.

You only get to ask one question per post. Re-post your second question.

John

My calculator said it, I believe it, that settles it