At The End Of The Day, A Shopkeeper Has 12 Tins Of Cat Food Left.this Is 3/13 Of The Number Of What He Had In The Begginning Of The Day. Calculate The Numbers Of The Tin He Had At The Begging Of The Day.

Mar 11, 2025 by ADMIN 204 views

**Mathematical Problem Solving: Uncovering the Initial Number of Tins**

Introduction

In this article, we will delve into a mathematical problem that involves proportions and algebraic equations. A shopkeeper starts the day with an unknown number of tins of cat food and ends the day with 12 tins. We are given that the 12 tins left at the end of the day represent 3/13 of the initial number of tins. Our goal is to calculate the initial number of tins the shopkeeper had at the beginning of the day.

Understanding the Problem

Let's break down the problem and understand what is given and what needs to be found. We are told that the shopkeeper has 12 tins of cat food left at the end of the day. This number represents 3/13 of the initial number of tins. In mathematical terms, we can write this as:

12 = (3/13) * x

where x is the initial number of tins.

Solving the Equation

To solve for x, we need to isolate x on one side of the equation. We can do this by multiplying both sides of the equation by 13/3, which is the reciprocal of 3/13.

x = 12 * (13/3)

To simplify this expression, we can multiply 12 by 13 and then divide by 3.

x = (12 * 13) / 3

x = 156 / 3

x = 52

Conclusion

Therefore, the shopkeeper had 52 tins of cat food at the beginning of the day. This is the solution to the problem, and it is obtained by using algebraic equations and proportions.

Real-World Applications

This type of problem has real-world applications in various fields, such as business, economics, and science. For example, in business, understanding proportions and algebraic equations can help managers make informed decisions about inventory levels and supply chains. In economics, proportions and algebraic equations can be used to model economic systems and make predictions about future trends. In science, proportions and algebraic equations can be used to describe physical phenomena and make predictions about future events.

Tips and Tricks

When solving problems like this, it's essential to read the problem carefully and understand what is given and what needs to be found. It's also crucial to use algebraic equations and proportions to solve the problem. Additionally, it's helpful to simplify expressions and use mathematical properties to make calculations easier.

Practice Problems

Here are a few practice problems to help you reinforce your understanding of proportions and algebraic equations:

A bakery has 15 loaves of bread left at the end of the day. This number represents 2/5 of the initial number of loaves. How many loaves did the bakery have at the beginning of the day?
A store has 20 boxes of toys left at the end of the day. This number represents 4/9 of the initial number of boxes. How many boxes did the store have at the beginning of the day?
A farmer has 30 bags of fertilizer left at the end of the day. This number represents 5/8 of the initial number of bags. How many bags did the farmer have at the beginning of the day?

Solutions

Let x be the initial number of loaves. Then, we can write the equation as:

15 = (2/5) * x

To solve for x, we can multiply both sides of the equation by 5/2, which is the reciprocal of 2/5.

x = 15 * (5/2)

x = (15 * 5) / 2

x = 75 / 2

x = 37.5

Therefore, the bakery had 37.5 loaves of bread at the beginning of the day.

Let x be the initial number of boxes. Then, we can write the equation as:

20 = (4/9) * x

To solve for x, we can multiply both sides of the equation by 9/4, which is the reciprocal of 4/9.

x = 20 * (9/4)

x = (20 * 9) / 4

x = 180 / 4

x = 45

Therefore, the store had 45 boxes of toys at the beginning of the day.

Let x be the initial number of bags. Then, we can write the equation as:

30 = (5/8) * x

To solve for x, we can multiply both sides of the equation by 8/5, which is the reciprocal of 5/8.

x = 30 * (8/5)

x = (30 * 8) / 5

x = 240 / 5

x = 48

Introduction

In our previous article, we solved a mathematical problem involving proportions and algebraic equations. A shopkeeper starts the day with an unknown number of tins of cat food and ends the day with 12 tins. We were given that the 12 tins left at the end of the day represent 3/13 of the initial number of tins. Our goal was to calculate the initial number of tins the shopkeeper had at the beginning of the day.

Q&A Session

Here are some frequently asked questions related to the problem, along with their answers:

Q: What is the initial number of tins the shopkeeper had at the beginning of the day?

A: The initial number of tins the shopkeeper had at the beginning of the day is 52.

Q: How did you solve the problem?

A: We used algebraic equations and proportions to solve the problem. We started by writing the equation 12 = (3/13) * x, where x is the initial number of tins. We then multiplied both sides of the equation by 13/3, which is the reciprocal of 3/13, to isolate x.

Q: What is the reciprocal of 3/13?

A: The reciprocal of 3/13 is 13/3.

Q: How do you multiply fractions?

A: To multiply fractions, you multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom).

Q: What is the difference between a numerator and a denominator?

A: A numerator is the number on top of a fraction, and a denominator is the number on the bottom of a fraction.

Q: Can you give an example of how to multiply fractions?

A: Yes, for example, to multiply 1/2 and 3/4, you would multiply the numerators (1 and 3) to get 3, and multiply the denominators (2 and 4) to get 8. The result is 3/8.

Q: What is the relationship between fractions and proportions?

A: Fractions and proportions are related in that a proportion is a statement that two ratios are equal. For example, the proportion 2/3 = 4/6 is true because the two ratios are equal.

Q: Can you give an example of how to use proportions to solve a problem?

A: Yes, for example, if a recipe calls for 2 cups of flour and you want to make half the recipe, you can use proportions to find out how much flour you need. Let x be the amount of flour you need. Then, you can write the proportion 2/4 = x/2. Solving for x, you get x = 1 cup.