SOLUTION: 1. A rectangle has a perimeter of 22 feet. A new rectangle is formed by doubling the width w and tripling the length. The new rectangle has a perimeter of 58 feet. What is the

Question 1041124: 1. A rectangle has a perimeter of 22 feet. A new rectangle is formed by doubling the width w and tripling the length. The new rectangle has a perimeter of 58 feet. What is the width and the length of the original rectangle?
2. An online music store allows people to download a single song or an entire album. All single songs cost the same and all albums cost the same. You pay $22.94 to download 5 songs and 1 album. The next time you pay $31.95 to download 3 songs and 2 albums. How much does the store charge for a song? for an album?
3.It costs $1.99 to purchase boxes of pencils and 2.99 to purchase boxes of pens. If it costs $30.87 for 13 boxes how many would you need to get of each?
4. The length of a rectangle is 4 inches longer than 2 times it�s width. If the perimeter is 20 inches what is its length?

Found 2 solutions by Boreal, JoelSchwartz:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
p=2L+2W=22 feet
Pnew=6L+4W=58
these are two equations in two unknowns.
multiply the top by -3
-6L-6W=-66
6L+4W=58, now add them, and the lengths disappear
-2W=-8
W=4 feet
The first rectangle is 2L=8=22; 2L=14, L=7 feet
The 7 x 4 original rectangle has a perimeter of 22 feet. ANSWER
triple length and double width and rectangle is 21 feet x 8 feet. That has a perimeter of 58 feet.
-------------------------------
5S+1A=22.94
3S+2A=31.95
multiply the top by -2
-10S-2A=-45.88
3S+2A=31.95
-7S= -13.93
S=$1.99
5(1.99)+A=22.94
A=$12.99
check by substituting into second equation
3(1.99)+25.98=5.97+25.98=$31.95
----------------------------------
This would be 1.99x+2.99(13-x), where x= number of boxes of pencils.
1.99x+38.87-2.99x=30.87
-x=-8
x=8 boxes of pencils
13-x=5 boxes of pens.
-------------------------
W=width
2W+4=length
perimeter = 2L+2W=2(2W=4)+2W=2W+4W+8=20
6W+8=20
6W=12
W=2
width is 2 inches
length is 2(2)+4=8 inches ANSWER
The perimeter is 20 inches

Answer by JoelSchwartz(130) (Show Source): You can put this solution on YOUR website!
1
L=the length of the first rectangle
w=the width of the first rectangle
p=2L+2w
22=2L+2w
11-w=L
58=4w+6L
58=4w+6(11-w)
58=4w+66-6w
58-66=-2w
-8=-2w
w=4
L=7
2
x=the cost to buy one song
y=the cost to buy one album
5x+y=22.94
y=22.94-5x
3x+2y=31.95
3x+2(22.94-5x)=31.95
3x+45.88-10x=31.95
-7x=31.95-45.88
-7x=-13.93
x=1.99
y=22.94-5*1.99
y=12.99
3
x=the number of pencil's bought
y=the number of pens bought
x+y=13
2.99y+1.99x=30.87
2.99(13-x)+1.99x=30.87
38.87-2.99x+1.99x=30.87
-x=30.87-38.87
x=8
y=5
4
L=the length of the rectangle
w=the width of the rectangle
L=4+2w
p=2L+2w
20=2L+2w
20=2(4+2w)+2w
20=8+4w+2w
20-8=6w
12=6w
w=2
L=8
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