Mathematics
Mathematics
Problem
A vendor bought some apples at ₹12 each and some pears at ₹15 each, spending a total of ₹990. He sold all the apples at ₹15 each and all the pears at ₹18 each, making a profit of ₹225. (a) Form two linear equations in the number of apples and pears purchased. (b) Solve the equations to find how many apples and how many pears the vendor bought. a. Form two linear equations in the number of apples and pears purchased. b. Solve the equations to find how many apples and how many pears the vendor bought.Intuitive explanation
This is a system of linear equations problem where you need to translate a real-world situation into math. The key insight is that you have two pieces of information—total spending and total profit—and two unknowns (number of apples and pears), so you can write exactly two equations. One equation captures the cost constraint, and the other captures the profit constraint; solving them together reveals the quantities. Think of it as finding the intersection point where both conditions are satisfied simultaneously.
Intuitive explanation
This is a system of linear equations problem where you need to translate a real-world situation into math. The key insight is that you have two pieces of information—total spending and total profit—and two unknowns (number of apples and pears), so you can write exactly two equations. One equation captures the cost constraint, and the other captures the profit constraint; solving them together reveals the quantities. Think of it as finding the intersection point where both conditions are satisfied simultaneously.