SOLUTION: Valerie walks from her home to her school. One fifth of the way there she finds a nickel. One-quarter of the rest of the way she finds a dime. If she is still 2 blocks from school

Question 238823: Valerie walks from her home to her school. One fifth of the way there she finds a nickel. One-quarter of the rest of the way she finds a dime. If she is still 2 blocks from school when she finds the dime, how many blocks did she walk from her home to her school? (Assume that all blocks are equal in length.)
So far I have the setup: x - 1/5x - 1/4....= 2
The solution in the back of the books says to multiply 1/4 by 4/5x but I do not understand why or where that 4/5x even comes from.
I also have a general question. In this problem, it says she is one-fifth at the first find and one-quarter at the second. That corresponds to 1/5 and 1/4. In a different problem I encountered, it said that a boy walking from a ballfield to school traveled one-quarter of the way and then took a cab home. However, in this problem, they setup one-quarter as 3/4. Why 3/4 instead of 1/4?
Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Valerie walks from her home to her school. One fifth of the way there she finds a nickel. One-quarter of the rest of the way she finds a dime. If she is still 2 blocks from school when she finds the dime, how many blocks did she walk from her home to her school? (Assume that all blocks are equal in length.)
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Let "x" be the number of blocks to the school.
She walks (x/5) blocks to get to the nickel.
Note: She has (4/5)x blocks to go to get to the school.
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She walks (1/4)(4/5)x = (1/5)x blocks to get to the dime.
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Equation:
distance to the nickel + distance to the dime + 2 blocks = total distance
(x/5) + (x/5) + 2 = x
(2/5)x + 2 = x
2 = (3/5)x
x = 10/3 = 3 1/3 blocks
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From her home to the school is 3 1/3 blocks.
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I also have a general question. In this problem, it says she is one-fifth at the first find and one-quarter at the second. That corresponds to 1/5 and 1/4.
Comment: That is 1/4 of the remaining distance.
The remaining distance is (4/5)x after she has already gone (1/5)x of the way.
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In a different problem I encountered, it said that a boy walking from a ballfield to school traveled one-quarter of the way and then took a cab home. However, in this problem, they setup one-quarter as 3/4. Why 3/4 instead of 1/4?
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Comment: After he had gone one-quarter he had three-quarters of the way to go.
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Cheers,
Stan H.

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