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...

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?

Expert Answers
hala718 eNotes educator| Certified Educator

 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 

enotechris eNotes educator| Certified Educator

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

cburr eNotes educator| Certified Educator

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

atyourservice | Student

Work the problem you backwards:

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?

6 x 2 = 12 x 2 = 24

24 is 2/3 of the money, there fore 1/3 is 12

12 x 3 = 36

revolution | Student

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