Math Problem Statement

A, B and C have Rs. 1250, Rs. 1700 and Rs 2100 respectively. They utilized the amount to purchase

three types of shares of price x, y and z respectively.

A purchased 20 shares of price x, 50 shares of price y and 30 shares of price z.

B purchased 44 shares of price x, 30 shares of price y and 60 shares of price z.

C purchased 12 shares of price x, 40 shares of price y and 100 shares of price z. find x,y,z.

Solution

Let’s break down the problem by setting up equations for the total amount spent by each person based on the number of shares they purchased and their prices.

Given:

  • A’s total amount = Rs. 1250
  • B’s total amount = Rs. 1700
  • C’s total amount = Rs. 2100

Let:

  • x = price per share of the first type of shares
  • y = price per share of the second type of shares
  • z = price per share of the third type of shares

Information on shares purchased:

  1. A purchased: 20 shares of x, 50 shares of y, and 30 shares of z. 20x+50y+30z=125020x + 50y + 30z = 1250

  2. B purchased: 44 shares of x, 30 shares of y, and 60 shares of z. 44x+30y+60z=170044x + 30y + 60z = 1700

  3. C purchased: 12 shares of x, 40 shares of y, and 100 shares of z. 12x+40y+100z=210012x + 40y + 100z = 2100

System of Equations

We now have three equations:

  1. 20x+50y+30z=125020x + 50y + 30z = 1250
  2. 44x+30y+60z=170044x + 30y + 60z = 1700
  3. 12x+40y+100z=210012x + 40y + 100z = 2100

We can solve this system of equations to find the values of xx, yy, and zz.

Solving the Equations

To simplify, we can use substitution or elimination methods to solve for xx, yy, and zz.

Let's proceed with solving these equations:

Step 1: Solve the equations

  1. Multiply equation 1 by 2 to match terms with equation 2: 40x+100y+60z=250040x + 100y + 60z = 2500

  2. Subtract equation 2 from this new equation: (40x+100y+60z)(44x+30y+60z)=25001700(40x + 100y + 60z) - (44x + 30y + 60z) = 2500 - 1700 4x+70y=800-4x + 70y = 800 Simplify by dividing by -4: x17.5y=200x - 17.5y = -200

3

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Math Problem Analysis

Mathematical Concepts

Linear Equations
System of Equations

Formulas

Linear equation: ax + by + cz = d
System of linear equations solving techniques

Theorems

Substitution Method
Elimination Method

Suitable Grade Level

Grades 10-12