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Oduvanchick [21]
2 years ago
12

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

nd 5 units of Y. Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z. Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z.in this process A and C earn Rs. 6000 and Rs. 13000 respectively. While B neither lose nor gain. Find the prices per unit of the three commodities by using appropriate method.
please help me!!
Mathematics
1 answer:
liubo4ka [24]2 years ago
6 0

Answer:

(x,y,z)=(1477, 1464, 1437)

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

<h3>Case-1:</h3>
  • Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
  • Mr.A earns Rs6000

So, the equation would be

3x  +  5y - 4z = 6000

<h3>Case-2:</h3>
  • Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
  • Mr B neither lose nor gain meaning he has made 0₹

hence,

2x   - 3y  +  z = 0

<h3>Case-3:</h3>
  • Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
  • Mr.C earns 13000₹

therefore,

- x    + 4y  +  6z = 13000

Thus our system of equations is

\begin{cases}3x  +  5y - 4z = 6000\\2x   - 3y  +  z = 0\\ - x    + 4y  +  6z = 13000\end{cases}

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

\begin{cases}3x  +  5y - 4z = 6000\\2x   - 3y  +  z = 0\end{cases}\\\begin{cases}2x   - 3y  +  z = 0\\ - x    + 4y  +  6z = 13000\end{cases}

Now solve the equation accordingly:

\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}

Solving the equation for x and y yields:

\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

\implies z= \dfrac{217000}{151}

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

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Allowance method entries
Feliz [49]

Using the Allowance Method, the relevant transactions can be completed in the books of Wild Trout Gallery as follows:

1. <u>Allowance for Doubtful Accounts</u>

Accounts                                          Debit       Credit

Jan. 1 Beginning balance                             $53,800

Jan. 19 Accounts Receivable                           2,560

Apr. 3 Accounts Receivable       $14,670

July 16 Accounts Receivable        19,725

Nov. 23 Accounts Receivable                         4,175

Dec. 31 Accounts Receivable       25,110

Dec. 31 Ending balance          $56,500

Dec. 31 Bad Debts Expenses                   $55,470

Totals                                        $116,005  $116,005

<u>Accounts Receivable</u>

Accounts                                          Debit               Credit

Jan. 1 Beginning balance           $2,290,000

Jan. 19 Allowance for Doubtful           2,560

Jan. 19 Cash                                                            $2,560

Apr. 3  Allowance for Doubtful                                14,670

July 16  Allowance for Doubtful                              19,725

July 16  Cash                                                             6,575

Nov. 23  Allowance for Doubtful         4,175

Nov. 23 Cash                                                             4,175

Dec. 31  Allowance for Doubtful                             25,110

Dec. 31   Sales Revenue            8,020,000

Dec. 31   Cash                                               $8,944,420

Dec. 31 Ending balance                                 $1,299,500

Totals                                        $10,316,735 $10,316,735

3. Expected net realizable value of the accounts receivable as of December 31 = $1,243,000 ($1,299,500 - $56,500)

Allowance for Doubtful Accounts ending balance = $40,100 ($8,020,000 x 0.5%)

<u>Allowance for Doubtful Accounts</u>

Accounts                                          Debit       Credit

Jan. 1 Beginning balance                             $53,800

Jan. 19 Accounts Receivable                           2,560

Apr. 3 Accounts Receivable       $14,670

July 16 Accounts Receivable        19,725

Nov. 23 Accounts Receivable                         4,175

Dec. 31 Accounts Receivable       25,110

Dec. 31 Ending balance           $40,100

Dec. 31 Bad Debts Expenses                  $39,070

Totals                                        $99,605   $99,605

4. a. Bad Debt Expense for the year = $39,070

4.b. Balance for Allowance Accounts = $40,100

4.c. Expected net realizable value of the accounts receivable = $1,259,400 ($1,299,500 - $40,100)

Data Analysis:

Jan. 19 Accounts Receivable $2,560 Allowance for Uncollectible Accounts $2,560

Jan. 19 Cash $2,560 Accounts Receivable $2,560

Apr. 3 Allowance for Uncollectible Accounts $14,670 Accounts Receivable $14,670

July 16 Cash $6,575 Allowance for Uncollectible Accounts $19,725 Accounts Receivable $26,300

Nov. 23 Accounts Receivable $4,175 Allowance for Uncollectible Accounts $4,175

Nov. 23 Cash $4,175 Accounts Receivable $4,175

Dec. 31 Allowance for Uncollectible Accounts $25,110 Accounts Receivable $25,110

Accounts Receivable ending balance = $1,299,500

Allowance for Uncollectible Accounts ending balance = $56,500

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