Word problem

Question

The perimeter of a badminton court is 128ft. After a game of badminton a players coach estimates that the player has runs total of 360ft, which is equivalent to five times the courts length plus seven times it's width. What are the deminsions of a standard badminton court.

Answer 1

I find it helpful to draw a rectangle and label L for length and W for width. The perimeter is 2 Lengths + 2 Widths = 128. Simplify the equation and solve for either variable (I choose to solve for L).

 

2L + 2W = 128  Perimeter

L + W = 64        Simplify

L = 64 - W        Solve for L

 

And 360 is equivalent to 5L + 7W.

5L + 7W = 360

 

Substitute the known variable into the second equation.

5(64 - W) + 7W = 360      Substitute

320 - 5W + 7W = 360       Combine like terms

320 + 2W = 360               Subtract 320 from both sides

2W = 40                          Divide from both sides

W = 20 ***

 

Substitute the known value back into the original equation.

L + (20) = 64      Subtract from both sides

L = 44 ****

 

 

Does that make sense?