Mathematics
Grade-8
Easy

Question

If quarter of the number is same as the five added to the number, then the number is

  1. fraction numerator negative 20 over denominator 3 end fraction
  2. 20 over 3
  3. fraction numerator negative 5 over denominator 3 end fraction
  4. 5 over 3

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: fraction numerator negative 20 over denominator 3 end fraction


In the question it is given that if quarter of the number is same as the five added to the number.
We have to find the unknown number.
Step 1: Convert the word problem into numerical equation.
x over 4 equals 5 plus x
Step 2: Multiply both sides by 4.
rightwards double arrow x over 4 cross times 4 equals left parenthesis 5 plus x right parenthesis 4
rightwards double arrow x equals 4 left parenthesis 5 plus x right parenthesis
Step 3: Solve the brackets on RHS.
rightwards double arrow x equals 20 plus 4 x
Bring
Step 4: Subtract both sides by x.
rightwards double arrow x minus x equals 20 plus 4 x minus x
rightwards double arrow 0 equals 20 plus 4 x minus x
Step 5: Solve the like terms on RHS.
rightwards double arrow 3 x plus 20 equals 0
Step 6: Subtract both sides by 20.
rightwards double arrow 3 x plus 20 minus 20 equals 0 minus 20
rightwards double arrow 3 x equals negative 20
Step 7: Divide both sides by 3.
rightwards double arrow fraction numerator 3 x over denominator 3 end fraction equals fraction numerator negative 20 over denominator 3 end fraction
rightwards double arrow x equals fraction numerator negative 20 over denominator 3 end fraction
So, the number is fraction numerator negative 20 over denominator 3 end fraction.
Therefore, the correct option is a, i.e., fraction numerator negative 20 over denominator 3 end fraction.

Quarter is the one forth or 1 fourth of a given quantity or number.

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