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 By: achieve_goal (offline)  Tuesday, June 11 2013 @ 05:35 AM CDT (Read 616 times)
achieve_goal

q1. Jason,Edward and Sam had a total of \$837. Jason had the least amount
of money. The ratio of Edward's money to Sam's money was 4:3 at first. Jason and Edward each spent 1/3 of their money.Given that the three boys had \$648left, how much did Jason have at first?

Q2.A large warhouse had a total of 2180 black, red and white T-shirt for sale.
The ratio of the number of black T-shirts to the number of red T-shirts was 3:1.
After 2/5 of the black T-shirts, 1/3 of the white T-shirts and none of the
red T-shirts were sold on the first day, there were 1504 T-shirts left.How many red
T-shirts did the warehouse have at first?

Q3.Atfirst,Ravi had \$200 more than Vincent. He gave 40% of his money to Vincent.
Vincent then gave 25% of his money to Ravi. In the end, Vincent had \$68 more than Ravi. How much did Vincent give Ravi?

Regular Member

Registered: 09/14/11
Posts: 102

 By: echeewh (offline)  Tuesday, June 11 2013 @ 08:53 PM CDT
echeewh

Hi there,

Following pls find my worked solutions:

Q1.

J + E + S = 837

E : S
4 : 3

J = 837 - 7p

Given that J and E each spent 1/3 of their money, the amounts left by E and J were ...

E = (2/3) × 4p = (8/3)p
J = (2/3) × (837 - 7p) = 558 - (14/3)p

Since the 3 boys had \$648 left,

(8/3)p + 3p + 558 - (14/3)p = 648
3p - 2p = 648 - 558
p --> 90

J (at first) = 837 - 7p
837 - 7p --> 837 - (7 × 90) = 837 - 630 = 207

Jason (J) had \$207 at first.

========

Q2.

B + R + W = 2180

B : R
3 : 1

W = 2180 - 4p

Given that (2/5)B and (1/3)W were sold, remaining T-shirts were ...

B = (3/5) × 3p = (9/5)p
W = (2/3) × (2180 - 4p) = (4360/3) - (8/3)p

Since there were 1504 T-shirts left,

(9/5)p + p + (4360/3) - (8/3)p = 1504
p + (9/5)p - (8/3)p = 1504 - (4360/3)
[(15 + 27 - 40)/15]p = (4512 - 4360)/3
(2/15)p --> (152/3)
1p --> (152/3) × (15/2) = 380

There were 380 Red T-shirts at first.

========

Q3.

<before>
V: 1p
R: 1p + 200

<process>
R gave 40% (2/5) of his money to V.

R gave V:
(2/5) R = (2/5) × (1p + 200) = (2/5)p + 80

<after>
V: 1p + (2/5)p + 80 = (7/5)p + 80
R: 1p + 200 - (2/5)p - 80 = (3/5)p + 120

<process1>
V gave 25% (1/4) of his money to R.

V gave R:
(1/4) V = (1/4) × [(7/5)p + 80] = (7/20)p + 20

<after1>
V: (7/5)p + 80 - (7/20)p - 20 = (21/20)p + 60
R: (3/5)p + 120 + (7/20)p + 20 = (19/20)p + 140

Given that Vincent had \$68 more than Ravi in the end,

V - R = 68
(21/20)p + 60 - (19/20)p - 140 = 68
(2/20)p = 68 - 60 + 140
(1/10)p --> 148
1p --> 1480

V gave R:
(7/20)p + 20 --> [(7/20) × 1480] + 20
= 518 + 20 = 538

Vincent (V) gave \$538 to Ravi (R)

==========

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: 625

 By: achieve_goal (offline)  Wednesday, June 12 2013 @ 08:14 AM CDT
achieve_goal

Hi, thank you for these maths solutions.

Regular Member

Registered: 09/14/11
Posts: 102

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