
Please help. Thanks in advance.
Please help. Thanks in advance.
PS36(a) Let total money at first be u
<——————————–u————————————->
[–30—][——(2/9)(u-30)—][————-(1/2)u————— ]
< Bag ><— file + pen —-><———Final left —————>
< —— (7/9)(u-30)————–>
30 + (2/9)(u-30) = (1/2) u or alternatively,
(7/9)(u-30) = (1/2)u
(7/9)u – (210/9) = (1/2)u
(7/9)u – (1/2)u = 210/9
(14u – 9u)/18 = 70/3
u = 70/3 x 18/5 = 84
Hence fraction of money spent on bag = 30/84 = 5/14
(b) Cost of file and pen = (2/9)(84-30) = 12
Let p be the cost of the file, then cost of pen = 1/3p
p + 1/3p = 12
(4/3)p = 12 => p = 12 x (3/4) = 9
File = 9, Pen = 1/3(9) = 3, Difference = 9-3 = 6
Hence File is $6 more than the Pen.
(a)
Assuming Helen has 9U money after spending $30 on a bag.
30 + 9U = total money
Given
30 + 2U = ½( total money) = ½ (30 + 9U) multiply both side by 2 gives
60 + 4U = 30 + 9U
5U = 30
U = 6
30/ (30+9*6) =30/84 = 5/14
So 5/14 is the fraction of the money Helen spent on the bag
(b)
Cost of the pen = 1/3 of cost of file
Or you can say if pen costs 1P, then the file cost 3P, the difference is 2P
1P + 3P = 4P = 2 * 6=12
P = 3
2P= 6
So the file costs $6 more than the pen.
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If Tom has 7U stamp yesterday, then she left with 4U stamps today after giving 3U to Alice.
And Alice has 8U of stamps today. She has 5U yesterday.
7U = 5U + 72
2U = 72
U = 36
Tom has 7 *36 = 252 stamps yesterday.
Checking
Alice has 252-72 = 180 stamps yesterday
252 * 3/7 =108
Tom has 252-108 = 144 stamps today
Alice has 180 + 108 = 288 stamps today twice of what Tom has today.
PS39 Alternative Solution:
Yesterday Today left New ratio
Tom u+72 (4/7)(u+72) (1/2) p
u+72 (8/7)(u+72) p
Alice u u + (3/7(u+72) p
(8/7)(u+72) = u + (3/7(u+72) ( x 7 for both sides)
8u + 576 = 7u + 3u +216
2u = 360
u = 180
Hence Tom has (180+72) = $252 yesterday.