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 munch, she would 3 times as much as Anne. How much money have they saved together?
A. $300
B. $400
C. $450
D. $625
E. $750
Let x = Anne's money
y = Katherine's money
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Anne = x - 150 = (1/3)y
Katherine = [2y = 3x]
To solve this problem, we need to set up a system of equations based on the given information. Let's assume the amount of money Anne has saved is A, and the amount Katherine has saved is K.
According to the first statement, "If Anne had $150 less, she would have exactly 1/3 as much as Katherine." This can be expressed as A - $150 = (1/3)K.
Similarly, according to the second statement, "If Katherine had twice as much, she would have three times as much as Anne." This can be expressed as 2K = 3(A + $150).
So, we now have a system of equations:
1) A - $150 = (1/3)K
2) 2K = 3(A + $150)
To solve the system, we can multiply Equation 1 by 3 to eliminate the fraction:
3(A - $150) = K
We can substitute this value of K in Equation 2:
2(3(A - $150)) = 3(A + $150)
6A - $900 = 3A + $450
6A - 3A = $450 + $900
3A = $1350
A = $450
Now, we can substitute the value of A back into Equation 1 to solve for K:
($450) - $150 = (1/3)K
$300 = (1/3)K
K = $900
Finally, to find the total amount of money they have saved together, we add A and K:
$450 + $900 = $1350
Therefore, the correct answer is C. $450