Mathematics
Grade-8
Easy

Question

The teacher asks the students to give an equation. The equations are as follows
Robert: 2 times a number is 2 greater than the number
Bob: 3 times a number is 3 is greater than the number
Col: 4 added to a number is the same as 5 added to a number
Sam: 4 times a number is the same as 5 times a number
The student who gave an equation that has 0 as the solution is

  1. Robert
  2. Bob
  3. Col
  4. Sam

hintHint:

An equation has a constant, variable and an equal to sign. It has two sides LHS and RHS. A linear equation in one variable is equation with only one variable and in which the highest degree is 1. Here, we have to find the value of unknown value, by operating both sides with the same number so that the equation will be balanced.

The correct answer is: Sam


In the question the teacher has given four different equations in word form.
We have find the student whose solution to the equation is 0.
Step 1: Convert word problem to numerical equation.
So, the equation for
Robert is 2x= 2+x          ..................(1)
Bob is 3x=3+x               ...................(2)
Col is 4+x= 5+x            ....................(3)
Sam is 4x= 5x               ...................(4)
In eq. 3 the unknown terms are same on both sides which on solving got cancelled. Thus, eq. 3 has no solution.
Bring all the terms containing variables in one side by operating same numbers on both sides to balance the equation.
Step 2: In eq.1 subtract both sides by x.
rightwards double arrow2x-x= 2+x-x
rightwards double arrow2x-x= 2
rightwards double arrowx= 2
So, the solution for eq. 1 is 2.
Step 3: In eq. 2 subtract each term by x.
rightwards double arrow3x-x= 3+x-x
rightwards double arrow3x-x= 3
rightwards double arrow2x= 3         ...................(5)
Step 4: In eq. 5 divide both sides by 2.
rightwards double arrow fraction numerator 2 x over denominator 2 end fraction equals 3 over 2
rightwards double arrow x equals 3 over 2
So, the solution for the equation 2 is 3 over 2.
Step 5: In equation 4 subtract both sides by 4x.
rightwards double arrow4x-4x= 5x-4x
rightwards double arrow0= 5x-4x
rightwards double arrowx=0
So, the solution for eq. 4 is 0.
therefore, the correct option is d, i.e., Sam.

A linear equation in one variable is equation with only one variable and in which the highest degree is 1. A linear equation has no solution if it has same terms on both sides of the equation. Like terms in an equation are the terms having same variable of same power in which the coefficient may not be the same whereas unlike terms are the terms which don't have same variable. Addition and subtraction are possible in like terms but not in unlike terms.

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