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 Need help in some Math questions.
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By: drstevewu (offline)  Monday, December 10 2012 @ 07:24 AM CST (Read 1550 times)  
drstevewu

Need some help in the following Math questions:

1. John fully filled 2 identical jugs with water and syrup. The ratio of the amount of water to the amount of syrup was 4:1 in the first jug and 7:2 in the second jug. She emptied both jugs into an empty container. Find the ratio of the amount of water to the amount of syrup in the container.

2. Candy, Adam and Eddy had a sum of money. At first, Candy had $57 less than Adam. After Candy spent 3/4 of his money, Adam spent 1/5 of his money and Eddy spent $80, Candy and Eddy have the same amount of money left. The amount of money Eddy has now is 1/9 of the total amount of money left. How much money did Candy have at first?

Thank You...

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By: echeewh (offline)  Monday, December 10 2012 @ 07:06 PM CST  
echeewh

Hey there,

Following pls find my worked solution:

*** - for alignment purpose

Q1

Jug A ***** Jug B
W : S ***** W : S
4 : 1 ****** 7 : 2

Since both Jugs are identical, the capacities are same.

Total parts in A: 4p + 1p = 5p
Total units in B: 7u + 2u = 9u

Multiply (Jug A) ratio 9x, (Jug B ) ratio 5x, giving same capacities to both jugs.

Jug A ***** Jug B
W : S ***** W : S
36 : 9 **** 35 : 10

Hence, in container,

W : S
71 : 19

===================

Q2

Apply <work backwards> method using model.

Given E has (1/9) of the total money left, so does C. Thus, A has (7/9) of the total money left.

<after>

C |--|
E |--|
A |--|--|--|--|--|--|--|

<process>
E: +80
A: +(1/5) of his money
C: +(3/4) of her money

A left with (4/5) of his money. So multiply 7 parts (p) 4x, giving 28 units (u).

<before>
note: each of these parts (p) below need multiply 4x to give the units (u).

C |--|--|--|--|<--- 57 ----> (4 × 4u = 16u)
E |--|<----- 80 ---->| **** (4u + 80)
A |--|--|--|--|--|--|--|------| (28u + 7u = 35u)
* <---- 7 × 4u ----><7u>

Given A - C = 57, we have ...

35u - 16u --> 57
19u --> 57
1u --> 3

C (at first) = 16u --> 16 × 3 = $48

==============

Trust these help.

Do let me know again if these are different from your Answerkey or if there's further clarification.

Cheers,
Edward

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By: drstevewu (offline)  Tuesday, December 11 2012 @ 01:49 AM CST  
drstevewu

Hey Edward, thank you very much. But I dont quite understand the following soultions:

"A left with (4/5) of his money. So multiply 7 parts (p) 4x, giving 28 units (u).

<before>
note: each of these parts (p) below need multiply 4x to give the units (u).

C |--|--|--|--|<--- 57 ----> (4 × 4u = 16u)
E |--|<----- 80 ---->| **** (4u + 80)
A |--|--|--|--|--|--|--|------| (28u + 7u = 35u)
* <---- 7 × 4u ----><7u> "

Why left 4/5 of his money needs to multiply 7 parts with 4x?
If so, why E is 4u +80 and not 4 x 80??

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By: echeewh (offline)  Tuesday, December 11 2012 @ 08:49 PM CST  
echeewh

Hi drstevewu,

Following pls find my clarifications:

Your Q:
Why left 4/5 of his money needs to multiply 7 parts with 4x?

My Response:
Quote from question - Adam spent 1/5 of his money.
This means A (Adam) would have (4/5) total of his money left in the end. So this is equivalent to the 7 parts (p) of money left for A (refer to <after> model>. Challenge is how to split / divide these 7p into 4 equal portions. Using common multiple of 7 and 4 will give 28, which means these 7p --> 28u. Hence, 1p --> 4u. This explains why each part (|--|) in the models is multiplied 4x.

Your Q:
If so, why E is 4u +80 and not 4 x 80??

My Response:
Quote from question - Eddy spent $80.
After E (Eddy) spent $80, E is left with 1p (see <after> model). Working backwards, E would have (1p + 80) at the start (see <before> model). And since 1p --> 4u, it becomes (4u + 80).

=============

Trust the above is clear.

Do let me know again if there's further clarification.

Kind regards,
Edward

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By: drstevewu (offline)  Wednesday, December 12 2012 @ 09:08 AM CST  
drstevewu

Hey Edward.

Yes, I got it now... Thank you so much for your help.


Cheers,
Steve Wu

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