2 difficult rational expression word problems

Question

I have two word problems that I am having trouble setting up and solving.  I am hoping someone out there can help me.

 

The first one says:

I bought a box of keychains that cost me $70.  I make a profit of $.75 on each keychain that I sell.  When I have sold all but 12 from the box, I have made back the money that I invested.

a.) How many keychains are in the box?

b.) What price am I selling each for?

 

The second says:

There are 2 bikers in a race; an expert biker, and a novice biker.  They are in a 5 mile race.  The expert biker gives the novice biker a .6 mile head start.  The expert biker rides 3 mph faster than the novice biker.  The expert biker finishes 2 minutes before the novice biker.  At what rate was the novice biker riding?

 

I hope someone can help me!

Thank you,

james

Answer 1

I bought a box of keychains that cost me $70. I make a profit of $.75 on each keychain that I sell. When I have sold all but 12 from the box, I have made back the money that I invested.
a.) How many keychains are in the box?
b.) What price am I selling each for?

 

Solution

let consider 

number of keychains in box=x

cost of each keychain  = y

 

Write an equation for each statement

 

I bought a box of keychains that cost me $70

 

x* y = 70                                             ---- eq 1

 

I make a profit of $.75 on each keychain that I sell

 

Price of keychain=y+0.75

 

When I have sold all but 12 from the box, I have made back the money that I invested.

 

 

(12)(y+0.75)=70               

12y+9=70

 

12y=61

 

y=5.08

 

x*y=70

x*5.083=70

x=13.77 

 

number of keychains in box=x = 13.77 ...as keychain can not be in decimal we consider it 14
cost of each keychain = y=5.08 =5