SOLUTION: 1. what are the dimensions of a rectangle ? when the perimeter is 50 feet and the length is 11 feet more than the width. 2. what is the length of a triangle that has a perimeter o

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Question 85908: 1. what are the dimensions of a rectangle ? when the perimeter is 50 feet and the length is 11 feet more than the width.
2. what is the length of a triangle that has a perimeter of 69 inches? the second side is 7 inches longer than the first side. the third side is 6 inches shorter than twice the length of the first side.
3. michelle collected $184 selling girl scou cookies. the money consisted of $1, $5, $10 bills. there were three times as many $1 bills as $5. if there were $60 bills, how many of each bill did she have?
Answer by praseenakos@yahoo.com(507) (Show Source):
You can put this solution on YOUR website!
1) Assume that width = x feet.

Then length = x +11 feet( given that length is 11 feet more than width)

Perimeter = 2( length + width)

Given, perimeter = 50 feet.

==> 2( length + width) = 50

==> 2( x + 11 + x ) = 50

==> 2( 2x + 11) = 50

==> 2*2x + 2*11 = 50

==> 4x + 22 = 50

Subtract 22 from both sides.....

==> 4x + 22 -22 = 50 - 22

==> 4x = 28

Divide both sides of the expression by 4

==>

===> x = 7

That is width = 7 feet.

So, length = x + 11 = 7 + 11 = 18 feet.

You can check yopur answer by plugging the values of length and width in the given formula, perimeter = 2(length + width)

2) Question:

a triangle has a perimeter of 69 inches. the second side is 7 inches longer than the first side. the third side is 6 inches shorter than twice the length of the first side. find the length of each side.

Answer;

Assume that the first side = x inches

The the second side is = (x+7) inches

The third side = 2x - 6 inches

Perimeter = total length of its sides = 69 inches

That is sum of three sides will give the perimeter....

==> x + x + 7 + 2x - 6 = 69

Now collect the x terms together.....
==> x+ x+ 2x + 7 - 6 = 69

==> 4x + 1 = 69

Subtract 1 from both sides.

==> 4x + 1 - 1 = 69 -1

==> 4x = 68

Divide both sides by 4

==>

==> x = 17

That is length of the first side = 17 inches

So second side = x + 7 = 17 + 7 = 24 inches.

Third side = 2x - 6 = 2*17 - 6 = 34 - 6 = 28 inches

3. michelle collected $184 selling girl scout cookies. the money consisted of $1, $5, $10 bills. there were three times as many $1 bills as $5. if there were $60 bills, how many of each bill did she have?
Answer:

Assume that there are 'x' $5 bills

Then there are '3x' $1 bills.

Since there are total 60 bills....
number of $10 bills are 60 - (x + 3x) = 60 -4x

Now total amount of money collected = $184

So we can write....as follows...

$5 * x + $1* 3x + $10*(60 - 4x) = $184

==> 5x + 3x + 600 - 40x = 184

==> 8x + 600 - 40x = 184

==> 600 - 32x = 184

Add 32x on both sides...

==> 600 - 32x + 32x = 184 + 32x

==> 600 = 184 + 32x

Subtract 184 from both sides......

==> 600 - 184 = 184 + 32x - 184

==> 416 = 32x

Divide both sides by 32

==>

==> 13 = x

That is number of $5 bills = 13

Number of $1 bills = 3*13 = 39

Number of $10 = 60 - 4*13

==> = 60 - 52 = 8

Hope you found the explanation useful....

Regards,

Praseena.