Linear Equations in Two Variables Word Problems

As we know that linear equations in two variables could be solved using substitution method or elimination method. Now let us learn some applications of simultaneous equations which occurs in our day to day life. we could describe the real situation problem in words, which  we call as word problem. Let us solve the linear equations in two variables word problems by following the steps below:

Read the problem unless you understand and find the unknown quantities which we have to calculate. Name the quantities with a variable name like a,b,c, x, y, z...

Determine which variables has to be solved.

understanding the problem, formulate the equations according to the problem. If two variables has to be solved we need two simultaneous equation.

Let uis solve the linear equation in two variables word problem using substitution method or elimination method.

 

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Linear Equations in Two Variables Word Problems Examples:

  • A gardening company placed orders with a nursery. One was for 13 bushes and 4 trees, and totalled $487. The second order was for 6 bushes and 2 trees, and totalled $232. The bill doesn't tell the amount of per item. What were the costs of one bush and of one tree?

Sol:

Let $x be the cost of one bush and $y be the cost of one tree.

So, 13x + 4y = 487

      6x + 2y = 232

On solving these two equations, we get x = 23 and y = 47

  • The area of a rectangle is reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Find the length and breadth of the rectangle.

Sol:

Let "l" be the length and"b" be the breadth of the rectangle.

Area = lb square units

area of a rectangle is reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units

lb - 9 = (l-5)(b+3)

`=>`

area is increased by 67 square units, if we increase the length by 3 units and breadth by 2 units

lb + 67 = (l+3)(b+2)

2l + 3b - 61 = 0

On solving these two equations we get l = 17 units and b = 9 units.

 

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Some Linear Equations in Two Variables Word Problems:

  • Half the perimeter of a garden, whose length is 4 more than its width is 36m. Find the dimensions of the garden.
  • The area of a rectangle is reduced by 67 square units if its length is increased by 3 units and the breadth is decreased by 4 units. If we decrease the length by 1 unit and breadth is increased by 4 units, the area is increased by 89 square units. Find the length and breadth of the rectangle.
  • Two men and 7 women can do a work in 4 days. the same work is done in 3 days by 4 men and 4 women. How long would it take one man and one women to do it?