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

You will have 5 but for 30 then 60

Answer 2

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=(y_(2)-y_(1) )/(x_(2)-x_(1) )\\ r=(15-5)/(3-1)=(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.