Madhu makes 3 bracelets and Swetha makes 2 bracelets. They both use the same number of string colors. How many colors should they used to make the same amount of money ?
Madhu’s Bracelet : Rs 5 per bracelet plus Rs 2 for each string color.
Swetha’s Bracelet : Rs 3 per bracelet and Rs 3 for each string color.
Say whether this situation has no solution or infinitely many solutions?

The correct answer is: Madhu and swetha should be using 9 color strings in total to make the same amount from the bracelets. Also, since the given situation has only 1 value of x that satisfies the given condition, the given situation has only 1 solution.

Step-by-step solution:-
Let the total number of string colors used by Swetha and Madhu be x.
Now, we know that for Madhu's bracelets-
Variable charge for Madhu's bracelet = Number of strings × Price per string
∴ Variable charge for Madhu's bracelet = x × 2 .......................................................... (As per given information)
∴ Variable charge for Madhu's bracelet = 2x .............................................................. (Equation i)
Cost of bracelets made by Madhu = Fixed charge per bracelet × number of bracelets made + Variable charge
∴ Cost of bracelets made by Madhu = 3 × 5 + 2x ............ (From given information & Equation i)
∴ Cost of bracelets made by Madhu = 15 + 2x ............................................................ (Equation ii)
Also, For Swetha's bracelets-
Variable charge for Swetha's bracelet = Number of strings * Price per string
∴ Variable charge for Swetha's bracelet = x × 3 .......................................................... (As per given information)
∴ Variable charge for Swetha's bracelet = 3x .............................................................. (Equation iii)
Cost of bracelets made by Swetha = Fixed charge per bracelet × Number of bracelets made + Variable charge
∴ Cost of bracelets made by Swetha = 2 × 3 + 3x ............ (From given information & Equation iii)
∴ Cost of bracelets made by Swetha = 6 + 3x ............................................................ (Equation iv)
As per the condition given in the question, we need to find the value of x for which the total cost of bracelets made by Madhu and Swetha are the same.
∴ Equating Equations ii & iv, we get-
15 + 2x = 6 + 3x
∴ 15 - 6 = 3x - 2x ..................................................................................................... (Taking all variables & constants on either sides of the equation)
∴ 9 = x
Final Answer:-
∴ Madhu and swetha should be using 9 color strings in total to make the same amount from the bracelets. Also, since the given situation has only 1 value of x that satisfies the given condition, the given situation has only 1 solution.