Question

Write an algebraic for each of the following:
The score of Ragini in Mathematics is 23 more than two-third of her score in English. If she scores $x$ marks in English, what is her score in mathematics?

Answer 1

Hint: We use the given variable for the marks obtained in English and assign another variable to the marks obtained in Mathematics. Equate the variable representing marks obtained in mathematics to two third of the marks obtained in English plus the given marks.
* If any number ‘a’ is two-third of another number ‘b’ then we can write \[a = \dfrac{2}{3}b\]. Two third is defined as two parts of the total three parts of any object which is being divided in the question.

Complete step-by-step answer:
We have marks obtained by Ragni in two subjects Mathematics and English.
We are given the marks obtained in English by Ragni as ‘x’.
Let us assume the score obtained by Ragni in mathematics as ‘y’.
Since we are given that the score of Ragni in Mathematics is 23 more than two-third of her score in English, we frame an equation representing the score in Mathematics.
\[ \Rightarrow \]Score of Ragni in mathematics \[ = 23 + \dfrac{2}{3}\] marks obtained by Ragni in English
Substitute the value of marks obtained by Ragni in English on RHS of the equation and value of marks obtained in mathematics in LHS of the equation.
\[ \Rightarrow y = 23 + \dfrac{2}{3}x\]
\[ \Rightarrow y = 23 + \dfrac{{2x}}{3}\]
Take LCM of the equation in RHS of the equation
\[ \Rightarrow y = \dfrac{{23 \times 3 + 2x}}{3}\]
Calculate the product in numerator in RHS of the equation
\[ \Rightarrow y = \dfrac{{69 + 2x}}{3}\]

\[\therefore \]Marks obtained by Ragni in Mathematics is \[\dfrac{{69 + 2x}}{3}\].

Note: Students make mistakes while shifting the values from one side of the equation to another side as they don’t change signs from negative to positive and vice versa. Also, while cross multiplying always brings the value of numerator to denominator and vice versa.