Question 522779


a. create two linear equations below that give the amount that each girl has nleft as a function of the number of games they have played. 



Total Amount Abbey has = $20
Number of games played = x
Game cost = 50 cents or $0.5
Amount spent on games = x*0.5=0.5x
Amount  with Abbey left = y = 20-0.5x....................(1)


Total Amount Blanca has = $22
Number of games played = x
Game cost = 75 cents or $0.75
Amount spent on games = x*0.75=0.75x
Amount left with Blanca = y =22-0.75x....................(2)

    
b. After how many games will the two girls have the same amount of money left? 


Amount left with Abbey = Amount left with Blanca
20-0.5x = 22-0.75x
0.75x-0.5x=22-20
0.25x=2
0.25x/0.25=2/0.25
x=8
After 8 games amount of money left with each of them will be equal. 


c. How much money do they have at this point?


Amount  with Abbey left = y = 20-0.5x....................(1)
Amount  with Abbey left = y = 20-0.5(8)
Amount  with Abbey left = y = 20-4
Amount  with Abbey left = y = $16


Amount left with Blanca = y =22-0.75x....................(2)
Amount left with Blanca = y =22-0.75(8)
Amount left with Blanca = y =22-6
Amount left with Blanca = y =$16



2) The length of a rectangle garden is three feet more than twice its width.


a. If the width of this garden is given by w then write an expression, in terms,for the length, l, of the garden.


l=2w+3


b. Write an expression, in terms of w, for the perimeter of the garden. Remember,the perimeter is the sum of the two widths and the two lengths.

p=2w+2l
Put the value of l in above equation
p=2w+2(2w+3)
p=2w+4w+6
p=6w+6
p-6=6w
(p-6)/6=6w/6
(p-6)/6=w
w=(p-6)/6
w=p/6-6/6
w=p/6-1


c. If the perimeter of the garden is 114 feet, then what is the width of the garden?

w=p/6-1
w=144/6-1
w=24-1
w=23 feet