A smartphone is made with 4 antennae, 4 microchips, 3 radios and 1 casing materi

Question

A smartphone is made with 4 antennae, 4 microchips, 3 radios and 1 casing material cost is $175. Each microchip costs twice as much as each radio, and each radio costs $10 less than each casing. Each casing costs as much as 2 antennae plus half of each radio. Set up the system of simultaneous equations linking the price of each component, and solve the equations, using the Gaussian Elimination method, to determine the price of each component Confirm that the total price of the smartphone adds up to $175.

Explanation / Answer

Let cost of antenna = a

Let cost of microchip = b

Let cost of radio = c

Let cost of casing= d

Given is:

4a + 4b + 3c + d = 175.... (1)

b = 2a.....(2)

c = d - 10...........3

d = 2a + c/2..........4

Putting 4 in 3 we get

c = 2a + c/2 - 10

c/2 = 2a - 10

c = 4a - 20.....(5)Putting this in 3 we get:

4a - 20 = d - 10

d = 4a - 10......(6)

Putting 2, 5 and 6 in 1 we get:

4a + 4 (2a) + 3 (4a - 20) + 4a - 10 = 175

4a + 8a + 12a - 60 + 4a - 10 = 175

28a - 70 = 175

32a = 245

a = 245/32

Similarly all can be calculated.

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