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By: sundarshoba (offline)  Saturday, February 07 2015 @ 03:23 AM CST (Read 1023 times)  
sundarshoba

Please assist,

1. Polly had 360 dolls more than Ariel at first. After Polly gave away 1/4 of her dolls and Ariel gave away 2/3 of her dolls, they had 764 dolls altogether. How many dolls did they give away altogether?

2. Jon, Molly and Chris shared some sweets.The ratio of the total number of sweets received by Jon and Molly to the total no of sweets received by Chris was 2:5. When Chris gave 25 sweets to Jon and 31 sweets to Molly, and Jon gave 12 sweets to Molly, each of them had the same number of sweets. Find the total number of sweets John had at first.

Thks

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By: echeewh (offline)  Saturday, February 07 2015 @ 05:24 AM CST  
echeewh

Hey <sundarshoba>,

Following are my worked solutions:

Q1.

Two methods can be used to solve this problem, (i) model (ii) simultaneous.

<Simultaneous> method is used here.

P - A = 360 -- (1)
(3/4)P + (1/3)A = 764 -- (2)

(2)x12:
9P + 4A = 9168 -- (3)

Comparing (1),(3) to eliminate A:
(1)x4:
4P - 4A = 1440 -- (4)

Comparing (3),(4):
(3)+(4):
13P = 10608
P = 10608 ÷ 13 = 816 -- (5)

Substitute (5) in (1):
816 - A = 360
A = 816 - 360 = 456

Total dolls at first = P + A
= 816 + 456 = 1272

Given there were 764 dolls left,
number of dolls given away = 1272 - 764 = 508

======

Q2.

*** - for alignment purpose

<Before>
(J + M) : C Total
2 : 5 ********* 7 -- (1)

<After>
J : M : C Total
1 : 1 : 1 *** 3 -- (2)

As this is an internal transfer process, total sweets (before) = total sweets (after) <Unchanged Total concept>. Hence, common multiple of 7,3 is 21.

(1)x3:
<Before>
(J + M) : C Total
6 : 15 ****** 21 -- (3)

(2)x7
<After>
J : M : C Total
7 : 7 : 7 ** 21 -- (4)

using <work backwards> method, we have ...

<Jon gave 12 sweets to Molly>
M: 7u - 12
J: 7u + 12

<Chris gave 25 sweets to Jon and 31 sweets to Molly>

<before>
M: 7u - 12 - 31 = 7u - 43 -- (5)
J: 7u + 12 - 25 = 7u - 13 -- (6)
C: 7u + 25 + 31 = 7u + 56 -- (7)

comparing (3),(7):
C:

15u = 7u + 56
8u --> 56
1u --> 56 ÷ 8 = 7

in (6):
J (at first) = 7u - 13 --> (7 × 7) - 13
= 49 - 13 = 36

=======

Trust this helps.

Do let me know again if this is different from the <answerkey> or if there's further clarification.

Cheers,
Edward

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