SOLUTION: The ratio of the length to the width of a rectangle is 5:4. If the length is increased by 8 and the width halved, the ratio of the length to the width of the new rectangle is 7:2.

Algebra ->  Proportions -> SOLUTION: The ratio of the length to the width of a rectangle is 5:4. If the length is increased by 8 and the width halved, the ratio of the length to the width of the new rectangle is 7:2.       Log On


   

Question 121488: The ratio of the length to the width of a rectangle is 5:4. If the length is increased by 8 and the width halved, the ratio of the length to the width of the new rectangle is 7:2. Find the dimensions of the original rectangle.
Answer by jaymore(5) About Me  (Show Source):
You can put this solution on YOUR website!
Let the denote length by L and Width by W
L:W=5:4.......(1)
New dimensions after length is increased by 8 and width halved
L+8:1/2W=7:2........equation (2)
Solve the two equations
L/W=5/4...multiply both sides by W
L=5/4W
L+8/1/2W=7/2....cross multiply
2(L+8)=7/2W...open parenthesis
2L+16=7/2W
Substitute 5/4W for L
2(5/4W)+16=7/2W
5/2W+16=7/2W...like terms together
7/2W-5/2W=16
2W/2=16..Divide by 2 on both sides
W=16
L=5/4W=5/4times16=20