
By: achieve_goal (offline) Tuesday, June 11 2013 @ 05:35 AM CDT (Read 601 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 Tshirt for sale.
The ratio of the number of black Tshirts to the number of red Tshirts was 3:1.
After 2/5 of the black Tshirts, 1/3 of the white Tshirts and none of the
red Tshirts were sold on the first day, there were 1504 Tshirts left.How many red
Tshirts 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 Tshirts were ...
B = (3/5) × 3p = (9/5)p
W = (2/3) × (2180  4p) = (4360/3)  (8/3)p
Since there were 1504 Tshirts 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 Tshirts 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

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Registered: 04/21/11 Posts: 623





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



