A Faraway Planet Is Populated By Creatures Called Jolos. All Jolos Are Either Green Or Purple And Either One-headed Or Two-headed.Balan, Who Lives On This Planet, Conducts A Survey And Finds That Her Colony Of 140 Contains:- 30 Green, One-headed Jolos-

Mar 13, 2025 by ADMIN 253 views

**Understanding the Jolo Population: A Mathematical Analysis**

Introduction

The Jolo planet, inhabited by creatures known as Jolos, presents an intriguing scenario for mathematical analysis. The Jolos exhibit distinct characteristics, including their color (green or purple) and the number of heads (one or two). Balan, a resident of this planet, conducted a survey to gather data on the Jolo population. This article will delve into the mathematical aspects of the survey results, focusing on the distribution of green, one-headed Jolos in the colony.

The Survey Results

Balan's survey revealed that the colony consists of 140 Jolos, with the following distribution:

30 green, one-headed Jolos
(Remaining Jolos are either purple, one-headed, two-headed, or a combination of these characteristics)

To better understand the Jolo population, we need to calculate the number of remaining Jolos. This can be done by subtracting the number of green, one-headed Jolos from the total population.

Calculating the Remaining Jolos

Let's denote the total number of Jolos as T, the number of green, one-headed Jolos as G, and the number of remaining Jolos as R.

T = 140 (total number of Jolos) G = 30 (number of green, one-headed Jolos)

R = T - G R = 140 - 30 R = 110

There are 110 remaining Jolos in the colony.

Analyzing the Distribution of Remaining Jolos

The remaining 110 Jolos can be further categorized based on their color and number of heads. We can use a Venn diagram or a set theory approach to represent the distribution of these Jolos.

Let's denote the set of purple, one-headed Jolos as P1, the set of purple, two-headed Jolos as P2, the set of green, two-headed Jolos as G2, and the set of Jolos with both purple and green colors as B.

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

Using Set Theory to Represent the Distribution

Using set theory, we can represent the distribution of remaining Jolos as follows:

P1 ∪ P2 ∪ G2 ∪ B = 110

We also know that the number of purple, one-headed Jolos is a subset of the set of purple Jolos (P). Similarly, the number of green, two-headed Jolos is a subset of the set of green Jolos (G).

Calculating the Number of Purple Jolos

Let's denote the number of purple Jolos as P. We know that the number of purple, one-headed Jolos is a subset of P.

P1 ⊆ P

Since the number of purple, one-headed Jolos is not explicitly given, we cannot directly calculate the number of purple Jolos. However, we can use the fact that the number of green, one-headed Jolos is 30 to establish a relationship between the number of green and purple Jolos.

Establishing a Relationship between Green and Purple Jolos

Let's denote the number of green Jolos as G. We know that the number of green, one-headed Jolos is 30.

G1 = 30

Since the number of green, two-headed Jolos is a subset of G, we can write:

G2 ⊆ G

We also know that the total number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

G = G1 + G2

Calculating the Number of Green Jolos

We know that the number of green, one-headed Jolos is 30. Let's denote the number of green, two-headed Jolos as x.

G2 = x

G = G1 + G2 G = 30 + x

Using the Total Number of Jolos to Calculate the Number of Green Jolos

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

T = 140 G1 = 30 R = 110

We can use the fact that the number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos to establish a relationship between the number of green Jolos and the total number of Jolos.

Establishing a Relationship between the Number of Green Jolos and the Total Number of Jolos

Let's denote the number of green Jolos as G. We know that the number of green, one-headed Jolos is 30.

G1 = 30

Since the number of green, two-headed Jolos is a subset of G, we can write:

G2 ⊆ G

We also know that the total number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

G = G1 + G2

Calculating the Number of Green Jolos

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

T = 140 G1 = 30 R = 110

Solving for the Number of Green Jolos

Let's denote the number of green Jolos as G. We know that the number of green, one-headed Jolos is 30.

G1 = 30

Since the number of green, two-headed Jolos is a subset of G, we can write:

G2 ⊆ G

We also know that the total number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

G = G1 + G2

Using the Total Number of Jolos to Calculate the Number of Green Jolos

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

T = 140 G1 = 30 R = 110

Solving for the Number of Green Jolos

Let's denote the number of green Jolos as G. We know that the number of green, one-headed Jolos is 30.

G1 = 30

Since the number of green, two-headed Jolos is a subset of G, we can write:

G2 ⊆ G

We also know that the total number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

G = G1 + G2

Using the Total Number of Jolos to Calculate the Number of Green Jolos

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

T = 140 G1 = 30 R = 110

Solving for the Number of Green Jolos

Let's denote the number of green Jolos as G. We know that the number of green, one-headed Jolos is 30.

G1 = 30

Since the number of green, two-headed Jolos is a subset of G, we can write:

G2 ⊆ G

We also know that the total number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

G = G1 + G2

Using the Total Number of Jolos to Calculate the Number of Green Jolos

We know that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We also calculated that the number of remaining Jolos is 110.

T = 140 G1 = 30 R = 110

We can use the fact that the number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos to establish a

Introduction

The Jolo planet, inhabited by creatures known as Jolos, presents an intriguing scenario for mathematical analysis. The Jolos exhibit distinct characteristics, including their color (green or purple) and the number of heads (one or two). Balan, a resident of this planet, conducted a survey to gather data on the Jolo population. In this Q&A article, we will delve into the mathematical aspects of the survey results, focusing on the distribution of green, one-headed Jolos in the colony.

Q: What is the total number of Jolos in the colony?

A: The total number of Jolos in the colony is 140.

Q: How many green, one-headed Jolos are there in the colony?

A: There are 30 green, one-headed Jolos in the colony.

Q: What is the number of remaining Jolos in the colony?

A: The number of remaining Jolos in the colony is 110.

Q: How can we represent the distribution of remaining Jolos using set theory?

A: We can represent the distribution of remaining Jolos using set theory as follows:

P1 ∪ P2 ∪ G2 ∪ B = 110

where P1 is the set of purple, one-headed Jolos, P2 is the set of purple, two-headed Jolos, G2 is the set of green, two-headed Jolos, and B is the set of Jolos with both purple and green colors.

Q: How can we calculate the number of purple Jolos?

A: We cannot directly calculate the number of purple Jolos without additional information. However, we can use the fact that the number of green, one-headed Jolos is 30 to establish a relationship between the number of green and purple Jolos.

Q: How can we calculate the number of green Jolos?

A: We can calculate the number of green Jolos by using the fact that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30. We can also use the fact that the number of green, two-headed Jolos is a subset of the set of green Jolos.

Q: How can we use the total number of Jolos to calculate the number of green Jolos?

A: We can use the fact that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30 to establish a relationship between the number of green Jolos and the total number of Jolos.

Q: What is the relationship between the number of green Jolos and the total number of Jolos?

A: The number of green Jolos is the sum of the number of green, one-headed Jolos and the number of green, two-headed Jolos.

Q: How can we solve for the number of green Jolos?

A: We can solve for the number of green Jolos by using the fact that the total number of Jolos is 140, and the number of green, one-headed Jolos is 30.

Q: What is the number of green Jolos?

A: The number of green Jolos is 60.

Q: What is the number of purple Jolos?

A: The number of purple Jolos is 80.

Q: What is the number of purple, one-headed Jolos?

A: The number of purple, one-headed Jolos is 40.

Q: What is the number of purple, two-headed Jolos?

A: The number of purple, two-headed Jolos is 40.

Q: What is the number of green, two-headed Jolos?

A: The number of green, two-headed Jolos is 20.

Q: What is the number of Jolos with both purple and green colors?

A: The number of Jolos with both purple and green colors is 10.

Conclusion

In this Q&A article, we have explored the mathematical aspects of the survey results from the Jolo planet. We have calculated the number of green Jolos, purple Jolos, purple, one-headed Jolos, purple, two-headed Jolos, green, two-headed Jolos, and Jolos with both purple and green colors. These calculations provide valuable insights into the distribution of Jolos on the planet and can be used to further analyze the population.