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In conjunction with the Olympic Games which was held in Tokyo, KOKUYO Company sold three types of souvenirs, that are keychains, calculators and pens. The company ordered its supply of souvenirs in two types of packets. The cost of a packet which consists of three keychains, and two calculators is RM45, whereas the cost of a packet which consists of a keychain, a calculator and a pen is RM40. The cost of a pen is four times the cost of a keychain. If the costs of a keychain, a calculator and a pen are RM x , RM y and RM z respectively, obtain a matrix equation to represent the above information. Hence, determine the cost of each type of souvenir supplied to the company.​

In conjunction with the Olympic Games which was held in Tokyo KOKUYO Company sold three types of souvenirs that are keychains calculators and pens The company o class=

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adioabiola

Here, we are required to obtain a matrix equation to represent the above information, and also determine the cost of each type of souvenir supplied to the company.

Therefore, the matrix equation is as follows:

  • 3x + 2y = 45............... equation 1
  • x + y + z = 40................ equation 2
  • z = 4x...................... equation 3

The prices of the souvenirs are;

  • RM5 for keychain
  • RM15 for calculator
  • RM20 for pens

First, for simplicity sake,

  • let x represent the cost of a keychain
  • let y represent the cost of a calculator
  • let z represent the cost of a pen.

To obtain a matrix equation to represent the information, we have;

  • The cost of a packet which consists of three keychains, and two calculators is RM45
  • i.e 3x + 2y = 45............... equation 1.

  • The cost of a packet which consists of a keychain, a calculator and a pen is RM40
  • i.e x + y + z = 40................ equation 2.

  • The cost of a pen is 4 times the cost of a keychain
  • i.e z = 4x...................... equation 3.

Therefore, the matrix equation is as follows:

  • 3x + 2y = 45............... equation 1
  • x + y + z = 40................ equation 2
  • z = 4x...................... equation 3

Now, to solve the matrix equation, there's a need to substitute 4x for z (as evident in equation 3) in equation 2. Therefore, equation 2 becomes,

x + y +4x = 40.

Therefore, 5x + y = 40.......,............. equation 4.

Also, it is possible to substitute y = 40 - 5x (from equation 4 above) for y in equation 1;

Then we obtain;

  • 3x + 2(40 - 5x) = 45
  • Therefore, 3x + 80 -10x = 45
  • Therefore, 7x = 35
  • Consequently, x = 5

Also, from equation 4,

  • y = 40 - 5x
  • y = 40 - 5(5),. y = 40 - 25
  • Therefore, y = 15

And finally, from equation 3, z = 4x

  • z = 4(5)
  • Therefore, z = 20.

Therefore , the prices of the souvenirs are;

  • RM5 for keychain
  • RM15 for calculator
  • RM20 for pens

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