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 By: elysius (offline)  Sunday, September 14 2014 @ 11:52 AM CDT (Read 1698 times)
elysius

1) Fiona has \$480 more than Shixiu. Shixiu gives Fiona 20% of her money. Fiona then gives 75% of her money to Shixiu. In the end, Shixiu has \$1892 more than Fiona. How much did Shixiu have at first?

2) Jonas and Richard had a total of 476 red marbles and 600 blue marbles. 40% of Jonas' marbles were red while the rest were blue. 50% of Richard's marble were red while the rest is blue. After exchanging some marbles with each other, Jonas had 32 more marbles than Richard. How many red marbles did Richard give to Jonas?

Newbie

Registered: 09/14/14
Posts: 2

 By: echeewh (offline)  Monday, September 15 2014 @ 01:12 AM CDT
echeewh

Hey <elysius>

Following are my worked solutions for Q1, Q3:

Q1.

F |--------------<- 480 ->|
S |--------------|

<S gives 20% to F>
S: -20% (1/5)

Since S gives (1/5) of her money to F, we can split the equal portion of F, S into 5u each. Hence, we have ...

<Before>
F: 5u + 480
S: 5u

<S gives 20% (1/5) to F>
(1/5) × 5u = 1u

<After>
F: 5u + 480 + 1u
= 6u + 480
S: 5u - 1u
= 4u

<F gives 75% (3/4) to S>
(3/4) × (6u + 480)
= (9/2)u + 360

<After1>
F: 6u + 480 - (9/2)u - 360
= (3/2)u + 120
S: 4u + (9/2)u + 360
= (17/2)u + 360

Given that Shixiu (S) has \$1892 more than Fiona (F) in the end, we have ...

S - F = 1892
(17/2)u + 360 - (3/2)u - 120 --> 1892
7u --> 1892 - 360 + 120 = 1652
1u --> 236

S (at first) = 5u
5u --> 5 × 236 = \$1180

======

Q3.

refer to diagram in question.

Given that W + Y = 2X,

SQ(uare) = W + X + Y + Z = 3X + Z -- (1)
SC(Semi Circle) = X + Y -- (2)
Q(uadrant) = Y + Z -- (3)

(2)-(3):
SC - Q = X - Z -- (4)

(1)+(4):
SQ + SC - Q = 3X + X = 4X
X = (SQ + SC - Q) ÷ 4

SQ = 56 × 56 = 3136

SC = (pi / 2) × 28 × 28
= [(22/7) × 28 × 28] ÷ 2
= 1232

Q = (pi / 4) × 56 × 56
= [(22/7) × 56 × 56] ÷ 4
= 2464

X = (SQ + SC - Q) ÷ 4
= (3136 + 1232 - 2464) ÷ 4
= 476 cm^2

=========

Trust these help.

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

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: echeewh (offline)  Monday, September 15 2014 @ 11:27 AM CDT
echeewh

Hey <elysius>,

One clarification is needed for Q2.

Appreciate if you can recheck this question as I think there is some missing info which is necessary for solving the problem.

For instance, the statement " Jonas had 32 more marbles than Richard " - is this referring to Red or Blue ??

Thank you so much .

Kind Rgds,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: elysius (offline)  Thursday, September 18 2014 @ 12:32 AM CDT
elysius

Hi Edward,

Appreciate your prompt replies for the two questions and Apologies for the omission for question 2

2) Jonas and Richard had a total of 476 red marbles and 600 blue marbles. 40% of Jonas' marbles were red while the rest were blue. 50% of Richard's marble were red while the rest is blue. After exchanging some marbles with each other, Jonas had 32 RED more marbles than Richard. How many red marbles did Richard give to Jonas?

Thank you!

Newbie

Registered: 09/14/14
Posts: 2

 By: echeewh (offline)  Thursday, September 18 2014 @ 08:47 AM CDT
echeewh

Thank you <elysius> for your clarification.

Following is my worked solution for Q2:

Total marbles = 476 + 600 = 1076

J(R) : J(B )
40 : 60
2 : 3

R(R) : R(B )
1 : 1

2p + 1u = 476 -- (1)
3p + 1u = 600 -- (2)

(2)-(1):
3p - 2p = 600 - 476
1p --> 124

Sub in (1)
1u = 476 - 2p
--> 476 - (2 × 124)
= 476 - 248
= 228

J(R) = 2p --> 2 × 124 = 248
J(B ) = 3p --> 3 × 124 = 372

R(R) = 1u --> 228
R(B ) = 1u --> 228

Given Jonas had 32 more red marbles than Richard after the exchange, we have ...

J(R) - R(R) = 32

And since this is an Internal transfer process, the total number of red marbles (before) = total number of red marbles (after) = 476.

<Red>
J |-----------<-32->|
R |-----------|

R(R) = (476 - 32) ÷ 2
= 222

228 - 222 = 6

Hence, Richard gave Jonas 6 Red marbles

========

Trust this helps.

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

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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