A man bought 50 dozen fruits consisting of apples and...

A man bought 50 dozen fruits consisting of apples and bananas. An apple is cheaper than a banana. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he had spent a total amount of $\mathrm{Rs} 1050$, find the number of dozens of apples and bananas he bought respectively. (1) 12 and 38 (2) 14 and 36 (3) 15 and 35 (4) 18 and 32

A man bought 50 dozen fruits consisting of apples and bananas. An apple is cheaper than a banana. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he had spent a total amount of $\mathrm{Rs} 1050$, find the number of dozens of apples and bananas he bought respectively.
(1) 12 and 38
(2) 14 and 36
(3) 15 and 35
(4) 18 and 32

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Key Concepts

Translating Word Problems into Equations

This concept involves reading a descriptive problem carefully and identifying the unknowns, then assigning variables to these unknowns so that relationships and conditions described in the problem can be expressed as algebraic equations.

System of Equations

This refers to a set of equations with multiple variables that are solved simultaneously. It is a key tool when multiple relationships constrain the values of the variables in a problem, allowing the solver to find a common solution that satisfies all conditions.

Substitution Method

This is a technique used to solve a system of equations by expressing one variable in terms of another from one equation and substituting this expression into the other equation(s). This method simplifies the process by reducing the number of variables in the equations.

Cost-Quantity Relationship

This concept involves setting up connections between the cost and quantity of items purchased. In many problems, the cost per unit and the number of units are linked through given relationships, and understanding this interplay is crucial to forming the correct equations.

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