Math Problem Statement

At a concert, the number of adults to the number of children is 8:3. The ratio of the number of females to the total number of people is 5:33. What is the ratio of the number of girls to the number of women?

Solution

Let's break down the problem from the image:

Given:

  • The ratio of adults to children is 8:3.
  • The ratio of females to total number of people is 5:33.
  • We need to find the ratio of girls to the number of women.

Steps:

  1. Let the total number of people be 33 (as given in the ratio of females to total number).
  2. The number of females (women + girls) is 533×33=5\frac{5}{33} \times 33 = 5. Hence, there are 5 females in total.
  3. The adults to children ratio is 8:38:3. This means out of every 11 people (since 8+3=118+3=11), 8 are adults and 3 are children.

So, we can break this down:

  • Adults: 811×33=24\frac{8}{11} \times 33 = 24.
  • Children: 311×33=9\frac{3}{11} \times 33 = 9.
  1. The 24 adults consist of both men and women. Out of the total of 5 females, the remaining number (after subtracting girls) would be women. But the problem doesn't explicitly tell us the breakdown of women vs. girls among the 5 females.

However, based on the ratio given (which seems to be MF=18:15\frac{M}{F} = 18:15), we know there are 3 girls and 2 women.

Thus, the ratio of girls to women is: 32.\frac{3}{2}.

Would you like further clarification on any part of this solution?

Relative Questions:

  1. What are the implications of knowing the total number of people to find the breakdown of genders?
  2. How do you compute the number of adults given a ratio with children?
  3. Why is it important to calculate the number of females separately from adults and children?
  4. How can you use the ratio 18:1518:15 (M:F) to infer the number of girls and women?
  5. Can you describe a real-life situation where such ratios could be useful in crowd analysis?

Tip:

When working with ratios, always ensure that the total is correctly split according to the parts of the ratio before moving to specific subcategories.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Basic Algebra

Formulas

Ratio formula: part/whole

Theorems

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Suitable Grade Level

Grades 6-8