Mathematics is a powerful tool for solving practical problems. In this article, we will explore a word problem involving a vendor who bought fruits and utilize mathematical principles, primarily the system of equations, to solve it. This approach not only helps to purchase and sell fruits efficiently but also demonstrates how to solve similar real-world problems.
Problem Statement
A vendor bought watermelons at P 150 each and pineapples at P 35 each. The vendor spent a total of P 7750 on these fruits and purchased a total of 90 pieces. Here, we will solve the problem step-by-step to find out how many pineapples and watermelons the vendor bought.
Step-by-Step Solution
Using Algebraic Equations
Let x be the number of pineapples and 90-x be the number of watermelons the vendor bought. We can set up the following equation:
35x 150(90-x) 7750
Expanding the equation:
35x 13500 - 15 7750
Combining like terms:
-115x 13500 7750
Isolating the variable x:
-115x 7750 - 13500
-115x -5750
Solving for x:
x 50
Therefore, the vendor bought 50 pineapples.
Using a System of Equations
Let's denote the number of watermelons by a and the number of pineapples by b. We can express the problem using two equations:
The total cost equation: a × 150 b × 35 7750 The total quantity equation: a b 90 which rearranges to a 90 - bSubstituting the value of a from the second equation into the first:
(90 - b) × 150 b × 35 7750
Expanding and simplifying:
13500 - 150b 35b 7750
Combining like terms:
13500 - 115b 7750
Isolating the variable b:
-115b 7750 - 13500
-115b -5750
Solving for b:
b 50
Therefore, the number of pineapples is 50, and consequently, the number of watermelons is 40.
Conclusion
Through the application of algebraic and system-solving techniques, we have determined that the vendor bought 50 pineapples and 40 watermelons. This approach not only solves the given problem but also provides a framework for solving a similar class of problems. Understanding these methods can be extremely useful in various real-world scenarios, from inventory management to financial planning.