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Question 245386: Need help please.
Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for both variables.
1.The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width?
2. 30,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $201,000. How many people paid $13.00 for reserved seats, and how many paid $4.00 for general admission?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
1.The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width?
:
L=original length, W=original width
The perimeter of a rectangle is six times the width.
:
perimeter:
2L + 2W = 6W
2L = 6W - 2W
2L = 4W
Simplify, divide both sides by 2
L = 2W
:
If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches.
2(L+4) + 2(W+7) = 160
2L + 8 + 2W + 14 = 160
2L + 2W + 22 = 160
2L + 2W = 160 - 22
2L + 2W = 138
Simplify, divide by 2
L + W = 69
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What are the length and the width?
From the 1st statement we know L=2W; replace L with 2W
2W + W = 69
3W = 69
W = 
W = 23 is the width
then
L = 2(23)
L = 46 is the width
:
:
Check solution in the 1st statement:
"The perimeter of a rectangle is six times the width."
2(46) + 2(23) = 6(23)
92 + 46 = 138;
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YOu can check the solution using the 2nd statement
"If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. "
:
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2. 30,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $201,000. How many people paid $13.00 for reserved seats, and how many paid $4.00 for general admission?
:
Let g = no. of general admission tickets
Let r = no. of reserved
:
Total attendance equation
g + r = 30000
or
g = (30000-r)
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Total receipts equation
4g + 13r = 201000
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Substitute (30000-r) for g in the above equation
4(30000-r) + 13r = 201000
120000 - 4r + 13r = 201000
9r = 201000 - 120000
9r = 81000
fr = 
r = 9000 reserved tickets sold
and
30000 - 9000 = 21000 general admission tickets
:
Check solution using the receipt equation
4(21000) + 13(9000) =
84000 + 117000 = 201000
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