SOLUTION: The areas of two similar rectangles add up to 39 square units. Twice the area of Rectangle A plus one-third the area of Rectangle B equals 33 square units. What are the areas of Re

Algebra ->  Rectangles -> SOLUTION: The areas of two similar rectangles add up to 39 square units. Twice the area of Rectangle A plus one-third the area of Rectangle B equals 33 square units. What are the areas of Re      Log On


   

Question 1014331: The areas of two similar rectangles add up to 39 square units. Twice the area of Rectangle A plus one-third the area of Rectangle B equals 33 square units. What are the areas of Rectangles A and B?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let a be the area of rectangle A.
let b be the area of rectangle B.

a + b = 39
2a + b/3 = 33

multiply the second equation by 3 and keep the first equation the same to get:

a + b = 39
6a + b = 99

subtract the second equation from the first to get:

-5a = -60

divide both sides of this equation by -5 to get:

a = 12

since a + b = 33, then b must be equal to 27

area of rectangle A is equal to 12.
area of rectangle B is equal to 27.

a + b = 12 + 27 = 39
this checks out ok.

2a + b/3 = 2*12 + 27/3 = 24 + 9 = 33
this checks out ok as well.

your solution is:

area of rectangle A is equal to 12 square units.
area of rectangle B is equal to 27 square units.