Simultaneous Equations Word Problems


If a set of equations with two or more variables are satisfied by a set of values, the values all called the solutions of the simultaneous equations.  If there is two variables, we need to have minimum two equations and if we have there unknowns, we need to have minimum three equations.  There many methods to solve those equations to ge the solutions.  These simultaneous equations have many applications.
Now let us see few problems on this topic simultaneous equations word problems.Example Problems on Simultaneous Equations Word Problems
Ex1: If sum of two numbers be 45 and their difference being 15, find the numbers.
Soln: let  x and y denote the numbers.
Given : x + y = 45 --------(1)
x – y = 15 -------(2)
Therefore (1) + (2) `=>` 2x = 60
`=>` x = 30
Therefore (1) `=>`30 + y = 45
`=>` y = 15.
Therefore the numbers are 30 and 15
Ex 2: If twice the son’s age in years is added to the father’s age, the sum is 70.  But if the father’s age is added to the son’s age, the sum is 95.  Find the ages of father and son.
Soln: let x and y be the ages of father and son
Given :    x + 2y = 70 ----------(1)
2x + y = 95   -----------(2)
Therefore 2 x (2) – (1) 4x +2y =190
-x –zy = -70
`=>` 3x = 120.
`=>` x = 40
Therefore (2)`=>`2 (40) + y = 95 `=>`  y = 15
Therefore the father’s age is 40 years and his son’s age is 15 years.
Ex 3: 2 tables and 3 chairs together cost 2000 dollars whereas 3 tables and 2 chairs together cost 2500 dollars.  Find the cost of a table and a chair.
Soln: Let x and y represents the princes of a table and a chair.
Given : 2x + 3y = 2000 ------------------(1)
3x+ 2y = 2500 -----------------(2)
Therefore 3 `xx` (2) – 2 `xx` (1)`=>` 9x + 6y = 7500
`=>` -4x +6y = -4000
`=>` 5x = 3500
`=>` x = 700 dallors
(1)`=>`2 (700) + 3y + 2000
`=>` 3y =600
`=>` y = 200 dollars
Therefore the cost of a table in 700 dollars and the chair is 700 dollars.Practice Problems on Simultaneous Equations Word Problems
1. 3 bags and 4 pens together cost 257 dollars whereas 4 bags and 3 pens together cost 324 dollars.  Find the cost of a bag and 10 pens
[Ans: 155 dollars]
2. The sum of the numerator and denominator of a fractions is 12.  if the denominator is increased by 3, the fraction becomes `1/2` .  Find the fraction
[Ans :` 5/7` ]