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Question 522779: hello, my name is arielena
These problems are about algebra 1 : linear word problems. I was wondering if you can help me solve a few linear problems ? or at least teach me how to solve problems like them ? My teacher doesn't teach very well and I don't understand a thing she teaches so please help . Thank you.
here's the 2 Im stuck on ..
1) Abbey and Blanca are playing games at the arcade in the mall. Abbey has $20 and is playing a game that costs 50 cents per game. Blanca arrived at the arcade with $22 and is playing a game that costs 75 cents per game.
a. create two linear equations below that give the amount that each girl has left as a function of the number of games they have played.
Let the number of games played = x.
A.____________ B.____________
b. After how many games will the two girls have the same amount of money left?
c. How much money do they have at this point?
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.
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.
c. If the perimeter of the garden is 114 feet, then what is the width of the garden?
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website!
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
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