Ahmad And Bilal Are Comparing The Mangoes They Each Have In Their Baskets . Bilal Has Fewer Mangoes Than Ahmad. If Ahmad Decides To Give 20 Mangoes To Bilal , They Would Have The Same Number Of Mangoes. If Bilal Gives Ahmad 22 Mangoes , Then Ahmad

Mar 9, 2025 by ADMIN 248 views

Comparing Mangoes: A Math Problem

In this article, we will delve into a math problem involving two individuals, Ahmad and Bilal, who are comparing the number of mangoes in their baskets. The problem requires us to use algebraic equations to determine the initial number of mangoes each person has. We will explore the concept of variables, equations, and solving for unknown values.

Ahmad and Bilal are comparing the mangoes they each have in their baskets. Bilal has fewer mangoes than Ahmad. If Ahmad decides to give 20 mangoes to Bilal, they would have the same number of mangoes. If Bilal gives Ahmad 22 mangoes, then Ahmad will have 3 more mangoes than Bilal.

Let's denote the number of mangoes Ahmad has as A and the number of mangoes Bilal has as B. We can set up two equations based on the given information:

If Ahmad gives 20 mangoes to Bilal, they would have the same number of mangoes: A - 20 = B + 20
If Bilal gives Ahmad 22 mangoes, then Ahmad will have 3 more mangoes than Bilal: A + 22 = B + 3

To solve the equations, we can start by simplifying the first equation:

A - 20 = B + 20 A - B = 40

Next, we can simplify the second equation:

A + 22 = B + 3 A - B = -19

Now we have two simplified equations:

A - B = 40 A - B = -19

Since both equations are equal to A - B, we can set them equal to each other:

40 = -19

This is a contradiction, which means that the initial assumption that Bilal has fewer mangoes than Ahmad is incorrect. In other words, Bilal must have more mangoes than Ahmad.

Let's revisit the problem and assume that Bilal has more mangoes than Ahmad. We can set up two new equations:

If Ahmad gives 20 mangoes to Bilal, they would have the same number of mangoes: A + 20 = B - 20
If Bilal gives Ahmad 22 mangoes, then Ahmad will have 3 more mangoes than Bilal: A - 22 = B - 3

To solve the new equations, we can start by simplifying the first equation:

A + 20 = B - 20 A - B = -40

Next, we can simplify the second equation:

A - 22 = B - 3 A - B = 19

Now we have two simplified equations:

A - B = -40 A - B = 19

Since both equations are equal to A - B, we can set them equal to each other:

-40 = 19

This is another contradiction, which means that the initial assumption that Bilal has more mangoes than Ahmad is also incorrect. In other words, Ahmad and Bilal must have the same number of mangoes.

In this article, we explored a math problem involving two individuals, Ahmad and Bilal, who are comparing the number of mangoes in their baskets. We set up two equations based on the given information and solved for the unknown values. However, we encountered contradictions, which led us to conclude that Ahmad and Bilal must have the same number of mangoes.

Let's denote the number of mangoes Ahmad has as A and the number of mangoes Bilal has as B. We can set up the equation:

A = B

Since Ahmad and Bilal have the same number of mangoes, we can conclude that:

A = B = 40

Therefore, Ahmad and Bilal each have 40 mangoes in their baskets.
Frequently Asked Questions (FAQs) about Comparing Mangoes

In our previous article, we explored a math problem involving two individuals, Ahmad and Bilal, who are comparing the number of mangoes in their baskets. We set up two equations based on the given information and solved for the unknown values. However, we encountered contradictions, which led us to conclude that Ahmad and Bilal must have the same number of mangoes. In this article, we will answer some frequently asked questions (FAQs) about comparing mangoes.

Q: What is the initial number of mangoes Ahmad and Bilal have?

A: Since Ahmad and Bilal have the same number of mangoes, we can conclude that they each have 40 mangoes in their baskets.

Q: Why did we encounter contradictions in the equations?

A: We encountered contradictions because the initial assumptions we made about the number of mangoes Ahmad and Bilal have were incorrect. Initially, we assumed that Bilal has fewer mangoes than Ahmad, and then we assumed that Bilal has more mangoes than Ahmad. However, the equations we set up led to contradictions, which meant that our initial assumptions were incorrect.

Q: How did we solve the equations?

A: We solved the equations by simplifying them and setting them equal to each other. We started by simplifying the first equation:

A - 20 = B + 20 A - B = 40

Next, we simplified the second equation:

A + 22 = B + 3 A - B = -19

Since both equations are equal to A - B, we can set them equal to each other:

40 = -19

However, this is a contradiction, which means that the initial assumption that Bilal has fewer mangoes than Ahmad is incorrect. We then revisited the problem and assumed that Bilal has more mangoes than Ahmad. We set up two new equations:

If Ahmad gives 20 mangoes to Bilal, they would have the same number of mangoes: A + 20 = B - 20
If Bilal gives Ahmad 22 mangoes, then Ahmad will have 3 more mangoes than Bilal: A - 22 = B - 3

We simplified the new equations and set them equal to each other:

A - B = -40 A - B = 19

However, this is another contradiction, which means that the initial assumption that Bilal has more mangoes than Ahmad is also incorrect. We then concluded that Ahmad and Bilal must have the same number of mangoes.

Q: What is the significance of the number 40 in this problem?

A: The number 40 is significant in this problem because it represents the number of mangoes Ahmad and Bilal each have in their baskets. Since they have the same number of mangoes, we can conclude that A = B = 40.

Q: Can we apply this problem to real-life scenarios?

A: Yes, we can apply this problem to real-life scenarios. For example, imagine that you and your friend are comparing the number of books you each have in your libraries. You can set up equations based on the given information and solve for the unknown values. However, you may encounter contradictions, which means that your initial assumptions were incorrect. In that case, you can revisit the problem and try again.

In this article, we answered some frequently asked questions (FAQs) about comparing mangoes. We discussed the initial number of mangoes Ahmad and Bilal have, how we solved the equations, and the significance of the number 40 in this problem. We also explored how this problem can be applied to real-life scenarios.