Algebraic Word Problem for the SAT with Solution

Today I would like to give a solution to the algebra SAT problem from last Wednesday. The original post can be found here: Algebraic Word Problem for the SAT

Level 5 Heart of Algebra

An ornithologist is in charge of a 400-acre bird sanctuary with only two types of birds: egrets and flamingos. There are currently 150 egrets and 200 flamingos living within the sanctuary. If 75 more egrets are introduced into the sanctuary, how many more flamingos must be introduced so that 5/6 of the total number of birds in the sanctuary are flamingos?

Algebraic solution: Let x be the number of flamingos that must be introduced. The number of flamingos will then be 200 + x and the total number of birds will be 150 + 75 + 200 + x = 425 + x. So, we must have (200 + x) = 5/6 (425 + x).

We multiply by 6 to get 6(200 + x) = 5(425 + x). Distributing on each side gives us 1200 + 6x = 2125 + 5x. Finally, we subtract 5x and subtract 1200 from each side of this last equation to get x = 925.

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