Question

Carol's profit at a craft fair is represented by the function p = 5b - 15, where p is the profit and b is the number of bracelets she sells. Kate's profit in shown in the table.
Bracelets sold (x)
1
2
3
4
Profit (in dollars) (y)

a. Compare the y-intercepts and rates of change.

b. How much will each girl make if she sells 30 bracelets?

Answer 1

Answer:

a. Compare the y-intercepts and rates of changes.

Remember that in the form $y=mx+b$, the coeffiecient of the variable is the rate of change, and the constant is the y-intercept.

In this case, we have the equation

$p=5b-15$

Where $p$ is the profit and $b$ is the number of bracelets. Her rate of change is $5 per bracelet and its y-intercept is at -15.

On the other hand, the table below represents Kate's profits

Bracelets sold (x)    Profit (in dollars) (y)

         1                                 5

         2                                10

         3                                15

         4                                20

First, we need to find the rate using the following formula and two pairs of the table (1,5) and (3,15)

$r=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ r=\frac{15-5}{3-1}=\frac{10}{2}\\ r=5$

The are of Kate's profist is 5 dollars per bracelet.

Now we use the point-slope formula

$y-y_{1} =m(x-x_{1} )\\y-5=5(x-1)\\y=5x-5+5\\y=5x$

This means the y-intercept is at zero.

If we compare, we would deduct that Carol's profit begins with -$15, while Kate's profit begins at $0, in other words, Carol has a debt. Also, both of them have the same rate of profit $5 per bracelet.

b. How much will each girl make if she sells 30 bracelets.

Carol would make

$p=5b-15=5(30)-15\\p=135$

$135 profit.

Kate would make

$y=5x=5(30)=150$

$150 profit.

So, Kate would make $15 more than Carol.

Answer 2

You will have 5 but for 30 then 60