Maths-

General

Easy

Question

# 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?

Hint:

### 1. Cost of bracelets = (Fixed charge per bracelet × number of bracelets made) + Variable charge

2. Variable charge = Number of color strings × Price per color string

## 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.

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