Question

Rohan spends \[x\] daily and saves \[y\] per week. What is his income in \[3\] weeks?
A). \[(21x+3y)\]
B). \[(3x+9y)\]
C). \[(21x+9y)\]
D). \[(7x+3y)\]

Answer 1

Hint: In this question we have given the daily expenditure of Rohan and per week savings of Rohan hence find the weekly expenditure of Rohan after that find the weekly income by adding savings and expenditure, then find out the income of three weeks and check which option is correct in the above given options.

Complete step-by-step solution:
Algebra is a generalised form of Arithmetic in the most basic sense. Algebra is a branch of mathematics concerned with the representation of a situation through the use of mathematical symbols, variables, and arithmetic operations such as addition, subtraction, multiplication, and division, which result in the development of appropriate mathematical expressions.
We only deal with numbers in Arithmetic. Different operations on numbers with a single definite value are included there.
However, we do not simply deal with numbers in algebra; we also deal with letters that represent different numbers. These letters can have any value we want to give them. The numerical values that a letter can represent are unrestricted.
Variables, literal numbers, or simply literals are the letters used in Algebra. In most cases, we operate letters or symbols in algebra without assigning any numerical value.
The unitary method is a method for determining the value of a single unit from the value of many units and multiple units from the value of a single unit. It's a method that we employ for the majority of math calculations. You can use this strategy to solve issues on ratio and proportion, algebra, geometry, and other subjects. We find the value of a single unit from the value of many units and the value of multiple units from the value of a single unit using the unitary technique.
We always count the value of a unit or one quantity first in the unitary approach, and then we calculate the values of more or less quantities. As a result, this procedure is called the unitary method.
Now according to the question we have given that:
Rohan’s daily expenditure is \[Rs.x\]
Therefore his weekly expenditure will be:
\[\Rightarrow Rs.7\times x\]
\[\Rightarrow Rs.7x\]
Rohan’s weekly saving is \[Rs.y\]
Hence his weekly income will be:
\[\Rightarrow \text{Weekly Income = Savings + Expenditure}\]
\[\Rightarrow \text{Weekly Income = 7x+y}\]
Therefore income in three weeks will be:
\[\Rightarrow 3\times \left( 7x+y \right)\]
\[\Rightarrow \left( 21x+3y \right)\]
Therefore we can conclude that option \[\text{(A)}\] is correct.

Note: Students you must note that multiplying the value of one quantity by the number of quantities yields the value of multiple quantities. By dividing the value of many quantities by the number of quantities, one can find the value of one and always write the things to be computed on the right-hand side and the things known on the left-hand side to simplify things.