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By: varsh (offline)  Thursday, October 24 2013 @ 09:00 PM CDT (Read 1457 times)  
varsh

please help me with this problem. Thanks in advance.


There were 310 phones and tabs for sale in a shop.All the phones in the shop cost $2484 more than all the tabs. After 1/3 of the phones and 10/11 of the tabs were sold, there were thrice as many phones as tabs left.If each phone cost $714 more than each tab,how much did each tab cost?

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By: echeewh (offline)  Thursday, October 24 2013 @ 10:52 PM CDT  
echeewh

Hello Varsh,

Appreciate if you can provide the <Answerkey> next time for verification purpose, if applicable. Thank you.

Following is my worked solution:

<After>

P |---|---|---|
T |---|

<Process>
P: (1/3) sold
T: (10/11) sold

Using <Work Backwards> method, the 3 parts in P <After> is the (2/3)P left. Common multiple of 3, 2 is 6. Hence, the above <After> model for P, T is multiplied 2x, as shown.

<After1>

P: 6u
T: 2u

After (2/3)P sold, (1/3)P left
(2/3)P left = 6u
(3/3)P <before> = 6 × (3/2) = 9u

After (10/11)T sold, (1/11)T left
(1/11)T left = 2u
(11/11)T <before> = 2 × 11 = 22u

Hence the <before> model is as follows:

<Before>

P: 9u
T: 22u

Given there were 310 phones and tabs,

31u --> 310
1u --> 10

Thus,
P = 9u --> 9 × 10 = 90
T = 22u --> 22 × 10 = 220

Given total cost of P is $2484 more than that of T,

90P - 220T = 2484 -- (1)


Given each phone (P) cost $714 more than each tab (T),

1P = 1T + 714
90P = 90T + (90 × 714) = 90T + 64260 -- (2)

Substitute (2) in (1), and we have ...

90T + 64260 - 220T = 2484
220T - 90T = 64260 - 2484
130T = 61776
T = $475.20

============

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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