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:
-
A purchased: 20 shares of x, 50 shares of y, and 30 shares of z.
-
B purchased: 44 shares of x, 30 shares of y, and 60 shares of z.
-
C purchased: 12 shares of x, 40 shares of y, and 100 shares of z.
System of Equations
We now have three equations:
We can solve this system of equations to find the values of , , and .
Solving the Equations
To simplify, we can use substitution or elimination methods to solve for , , and .
Let's proceed with solving these equations:
Step 1: Solve the equations
-
Multiply equation 1 by 2 to match terms with equation 2:
-
Subtract equation 2 from this new equation: Simplify by dividing by -4:
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
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