A research student wants to buy resistors, capacitors, and inductors for his lab

Question

A research student wants to buy resistors, capacitors, and inductors for his lab. His advisor tells him that he would be granted $100 for lab supplies only if the student can buy exactly 100 (total) pieces of resistors, capacitors, and inductors for exactly $100.

The only rule is that at least one of each kind of component--resistors, capacitors, and inductors--had to be purchased. Each resistor costs $10, each capacitor costs $3, and each inductor costs $0.5. How many of each kind of component did the student buy?

Explanation / Answer

let Number of resistors = R
let Number of capacitors = C
let Number of inductors = L

Given R + C + L = 100 ( total must be 100. )
and
      10R + 3C + 0.5L = 100 (total price must be 100)
      20R + 6C + L = 200
      R +   C + L = 100
  
      19R + 5C = 100     since minimum amount we have to buy must be 1 .
      Possible combinations will be as follows.
      if R = 1 then, 5C = 100-19 = 81 C will be fraction which is not possible.
      if R = 2 then, 5C = 100-38 = 62 C will be fraction which is not possible.
      if R = 3 then, 5C = 100-51 = 49 C will be fraction which is not possible.
      if R = 4 then, 5C = 100-76 = 24 C will be fraction which is not possible.
      if R = 5 then, 5C = 100-95 = 5 C = 5/5 = 1
      L = 100 - R - C = 100 - 5 - 1 = 100 - 6 = 94
  
      so Number of resistors = 5
         Number of capacitors = 1
       Number of inductors = 94
      
       CROSSCHECK:
      
       5 + 1 + 94 = 100
      
       5*10 + 1*3 + 94*0.5 = 50+3+47 = 100
     

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