Question

Danica and Darrelle have developed a lucrative business selling handmade silver bracelets. darrelle makes the more complex bracelets and danica makes the simpler ones. it takes darrelle 4 hours to make 3 bracelets and danica can make 5 bracelets every 4 hours
a. Convert this scenario into linear equation(s); show both the standard form and the slope-intercept form of your equation(s).
b. Could any part of this scenario be graphed using any of the special functions discussed in the course text? Explain your answer.
c. Each bracelet Darrelle sells makes $10.50 in profit. Each bracelet Danica sells makes $3.50 in profit. If Darrelle and Danica work the same amount of time, explain each of the steps you will use and then calculate how many hours will it take for the whole business to make at least $500 profit?

Answer 1

x= bracelets of darelle
y= bracelets by danica

a)set up some ratios
darel
3 brac. in 4 hrs. so
x/3=h/4 cross mult.
4x=3h subtract 3h both
4x-3h=0 this standard form
x=3/4 h slope-intercept form

danica
5 brace. in 2hrs
y/5 = h/2
2y + 5h = 0 standard
y=5/2 h slope- intercept


b)we do know what you studied in class

c) let p = profit
p = 10.50x + 3.50y ... profit in terms of bracelets produced
p = 10.50*((3/4)h) + 3.50*((5/2)h) .profit in terms of hours, where both work the same hours
p = 16.625 h

how many hours to 500$ profit
500= 16.625 h