Anne and Katherine are both saving money
from their summer jobs to buy bicycles. If
Anne had $150 less, she would have exactly 1/3
as much as Katherine. And if Katherine
had twice as much, she would have exactly
3 times as much as Anne. How much
money have they saved together?
( Choose the correct choice from the following answers:
A) $ 300
B) $ 400
C) $ 450
D) $ 625
E) $ 750

Rationale: if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a – 150 ) = k 3 a – 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a – 450 for k into the last equation and solve for a 2 ( 3 a – 450 ) = 3 a 6 a – 900 = 3 a – 900 = – 3 a 300 = a now substitute 300 for a into the same equation and solve for k : 2 k = 3 ( 300 ) 2 k = 900 k = 450 thus , together anne and katherine have 300 + 450 = 750 correct answer e ) $ 750
Answer: E