Question

A fabric cotton and synthetic fibres are in the ratio 2 :3 by weight. If the

weight of the cotton fibres is 30 grams. Express this statement as a linear

equation in two variables

a. 3x-2y =0
b. 3x+2y =0
c. 2x-3y = 0
d. 3x-2y = 30
FULL ANSWER​

Answer 1

Answer:

3x-2y = 30

total weight is 30

Answer 2

Given:

Weight of Fabric Cotton and Synthetic fiers are in the ratio 2:3.

Cotton weighs 30grams.

To Find:

The linear equation in two variables using the statements.

Solution:

The given problem can be solved by using mathematical operations.

1. It is given that the ratio of Weights of Cotton and Synthetic fibers is in the ratio 2:3.

2. Let the weight of cotton be x and the weight of synthetic fibers be y.

•   Using the condition from statement 1 we get,    

    =>   (x/y) = (2/3) (Consider it as equation 1).

3. It is further mentioned that the weight of cotton is 30 grams i.e, x=30grams.

4. On substituting the value of x in Equation 1 we get,

  => (30/y) = (2/3) (Solve for y).

  => y = (90/2)

  => y = 45 grams (weight of synthetic fibres are 45 grams).

5. Therefore the weight of cotton and synthetic fibers are 30 and 45 respectively.

6. To form a linear equation, of the form ax +by =0 where x and y are 30 and 45 respectively, Start applying the trial and error method.

•    By trial and error method, we get the values of a and b as (3,-2) or (-3,2).  

•    Therefore, the linear equations are 3x-2y = 0 or 2y - 3x =0.

7. Linear Equation can also be found directly from equation 1, by solving into simpler terms,    

  => 3x = 2y ,

  => 3x - 2y = 0 (OR) 2y - 3x = 0.

Hence, The linear equation in two variables is 3x - 2y =0 i.e, Option A is correct.