Writing Linear Equations-2

The perimeter of a square is 40 inches. Want perimeter of an equilateral triangle whose sides each measure the same length as the side of the square.
• A square has four sides so: S + S + S + S = 40
• 4S = 40
• S = 40/4 = 10 inches
• An equilateral triangle has three sides of equal length (see back of text).
• If each side is 10 inches long we have 10 + 10 + 10 = 30 inches, which is the answer we sought.

Coins are found.
• There are equal numbers of nickels and quarters.
• Let the number of nickels and quarters each equal x.
• There are twice as many half dollars as quarters.
• The number of quarters is 2x
• Money found has a total value of $2.60
• Let's build a table of the information

• Value of coin	Number of coins	Total Value
  0.05	x	0.05x
  0.25	x	0.25x
  0.50	2x	0.50(2x)
  Totals	5x	$2.60

• Using the fact that total value = $2.60 (and the last column of the table) we can write
• 0.05x + 0.25x + 0.50(2x) = 2.60
• 0.30x + x = 2.60
• 1.3x = 2.60
• x = 2.60/1.3 = 2 and 2x = 2*2 = 4
• So, we have 2 nickels, 2 quarters and 4 half dollars.
• This is 2(.05) + 2(.25) + 4(.50) = .10 + .50 + 2.00 = $2.60 which is correct

We want to find the measure of each of the angles in the triangle pictured above.

We know that the sum of the angles in a triangle is 180^o.
• (x + 15) + (10x - 20) + (x + 5) = 180
• 12x = 180
• x = 180/12 = 15
• Angles are:
• (x + 15) = 15 + 15 = 30 degrees
• (10x - 20) = 10*15 - 20 = 130 degrees
• (x + 5) = 15 + 5 = 20 degrees
• Total of all the angles is 30 + 130 + 20 = 180 degrees as it should