Question 65635: Solve each of the following problems. Be sure to show the equation used for the solution.
Social science. In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?
Geometry. The length of a rectangle is 2in. more than twice its width. If the perimeter of the rectangle is 34 in., find the dimensions of the rectangle.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the number of votes received by the losing candidate, then the winning candidate received x+220 votes. The sum of theses two amounts equal 810.
x+(x+220) = 810 Simplify and solve for x.
2x+220 = 810 Subtract 220 from both sides.
2x = 590 Divide both sides by 2.
x = 295
The losing candidate received 295 votes.
The winning candidate received 295+220 = 515 votes.
Check:
295 + 515 = 810
Let L = length and W = width.
L = 2W+2
The perimeter of a rectangle is given by:
P = 2L+2W Subtitute L = 2W+2 and P = 34 then solve for W.
34 = 2(2W+2) + 2W Simplify.
34 = 6W+4 Subtract 4 from both sides.
30 = 6W Divide both sides by 6.
W = 5
L = 2W+2 = 2(5)+2 = 10+2 = 12.
The dimensions of the rectangle are:
Length = 12 inches and the width = 5 inches.
Check:
P = 2L+2W
P = 2(12)+2(5)
P = 24+10
P = 34 inches.
|
|
|
