Question

Suppose you work at a retail store that sells teddy bears. You always work 40 hours a week. The amount of your weekly paycheck is a flat $300 for the 40 hours of work plus $5 for each teddy bear you sell. Let x be the number of teddy bears that you sell and f(x) be the amount of money you earn each week. Please answer the following questions:
a.Write an expression for f(x)

b.What is a reasonable domain for this function?

c.What does f(20) mean in the context of this problem?

d.How much money do you earn if you sell 25 teddy bears in a week?

e.How many bears do you need to sell if you want to make $500 in one week?

Please Explain

Answer 1

a. Remember that f(x) is the amount of money you earned each week. Also note that teddybears = x

f(x) = 5x + 300 is your equation

5x + 300 is your expression

-----------------------------------------------------------------------------------------------------------------

b. A reasonable domain can be 0 < x < 50, in which x is the amount you sell. 50 is a bit far out, but it takes into account holidays, as well as places you may sell at that have large amount of people.

-----------------------------------------------------------------------------------------------------------------

c. f(20) means that you sold 20 teddy bears, as 20 replaces x, which (like what was stated above) is the amount you sell

-----------------------------------------------------------------------------------------------------------------

d. Plug in 25 for x.

5x + 300 = t (total amount you make)

5(25) + 300 = t

Remember to follow PEMDAS. First, multiply 5 with 25

5 x 25 = 125

Next, add

125 + 300 = t

t = 425

$425 is the amount you make in a week.

-----------------------------------------------------------------------------------------------------------------

e. Note that you make $425 if you sell 25 teddy bears. Also remember that you are paid a flat $300. Remember the formula:

f(x) = 5x + 300

Plug in 425 for f(x)

425 = 5x + 300

Isolate the x. Do the opposite of PEMDAS. Note the equal sign. What you do to one side, you do to the other.

First, subtract 300 from both sides

425 (-300) = 5x + 300 (-300)

425 - 300 = 5x

125 = 5x

Next, divide 5 from both sides

(125)/5 = (5x)/5

x = 125/5

x = 25

25 teddy bears must be sold

-----------------------------------------------------------------------------------------------------------------

hope this helps