Select the correct alternative from the given choices. The...

Select the correct alternative from the given choices. The ratio of the number of students in three classes $A$, $B$ and $C$ is $3: 7: 8$. If ten students, are transferred from $C$ to $B, B$ will have 80 students. Find the total number of students in the three classes. (A) 150 (B) 160 (C) 180 (D) 210

Select the correct alternative from the given choices.
The ratio of the number of students in three classes $A$, $B$ and $C$ is $3: 7: 8$. If ten students, are transferred from $C$ to $B, B$ will have 80 students. Find the total number of students in the three classes.
(A) 150
(B) 160
(C) 180
(D) 210

Key Concepts

Word Problem Analysis

Analyzing word problems requires careful interpretation of the problem statement to identify known quantities, relationships, and required operations. This includes recognizing the impact of transferring quantities on the overall total and establishing the steps needed to reach the solution, such as setting up and solving equations based on the provided information.

Linear Equations

Linear equations are used to solve for unknown variables in situations with given additive or subtractive conditions. Once the problem has been modeled algebraically using ratios, any changes—such as transferring quantities between groups—can be incorporated into a linear equation. Solving these equations allows for the determination of the common factor or unknown quantities.

Algebraic Representation

Algebraic representation translates verbal descriptions into mathematical expressions. In the context of ratio problems, this typically involves assigning a variable (like x) to the common multiplying factor so that each part of the ratio can be expressed (e.g., 3x, 7x, 8x). This step is crucial for formulating equations that reflect the relationships described in the problem.

Ratio and Proportion

This concept involves expressing the distribution of quantities in relative terms. In problems where a ratio such as 3:7:8 is given, a common factor is used to represent each quantity algebraically. Understanding ratios allows one to set up expressions that proportionally relate parts to the whole, which is essential in accurately modelling the situation.

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