Question

You are buying packages of beads to make bracelets. Each package costs $3 plus 7% tax. You have a gift card for $15, and you plan to use only the gift card to pay for the beads. Which function c(p) represents the total cost, where p represents the number of packages of beads you purchase? What is a reasonable domain?

Answer 1

Explanation:

The funtion is:

C(p)= 3(p)+1.07 (1)

where: 3 is the package cost, p is the number of packages and 1.07 is the taxes

the cost could be equal or less than the gift card value so:

C
`C \leq 15` (2)

Replace 2 en 1

`15\leq 3(p)` x 1.07

3(p)
`\leq`
`(15)/(1.07)`

`3p [tex]\leq`14.02\\\\p\leq \frac{14.02}{3} \\\\p\leq 4.67[/tex]

It´s important to aprox the quantity to the minimum value so I can buy 4 packages

The reasonable domain is for all R because any number is a possible value of the independent variable