Barbara had some money saved. She spent one-third of it on a birdhouse. She spent half the remainder at the science museum.(continued down)
She bought a book about kayaking with half of what was left. When she got home, she still had $6. How much money did she have to start with?
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lets say the total money she had is X
1st she spend 1/3 of the money then the remaining is 2/3 x
then she spend 1/2 of the remaining which is 1/2 (2/3)x = 1/3x then the remaining which is 1/3x
then she spend half of the 1/3 which is 1/2 (1/3) = 1/6
the remaining is (1/6)x = 6 then x = 36 dollars
Let's work backwards.
You say she spent half of the remainder on kayaking, so the other half would be 6 dollars,
so the total remainder would be 6*2= 12 dollars
Next, there is also another "remainder" and she spent half of the other remainder on science trip, so 12*2= 24 dollars
Finally, she spent 1/3 of money saved on birdhouse, and the other 2/3 would have been the first remainder which is 24 dollars.
2/3 of money= 24 dollars
1/3 of it= 24/2= 12 dollars
total amount saved= 12*3= 36 dollars
The second answer is correct. The mistake in the first answer is that it should have been 1/2 * 1/2 * 2/3 x = 6
1/2 * 1/2 * 1/3 x = 6
1/12 x = 6
1/2 * 1/2 * 1/3(72) = 6
1/4 * 24 = 6
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