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Barbara had some money saved. She spent one-third of it on a birdhouse. She spent half...

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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?

Posted by mjoo-4 on December 3, 2008 at 11:32 AM via web and tagged with math, math algebra

High School Teacher

(Level 1) Educator Emeritus

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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

Posted by hala718 on December 4, 2008 at 1:50 AM (Answer #1)

College Teacher

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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

Posted by revolution on July 17, 2010 at 9:40 PM (Answer #2)

Middle School Teacher

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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

Posted by cburr on December 4, 2008 at 8:51 AM (Answer #3)

College Teacher

(Level 2) Senior Educator

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1/2 * 1/2 * 1/3 x = 6

1/12 x = 6

x=72 dollars

Check:

1/2 * 1/2 * 1/3(72) = 6

1/4 * 24 = 6

6=6

Posted by enotechris on December 3, 2008 at 11:46 AM (Answer #4)