Math Problem Statement

People were asked if they own a pet. 3/4 of those asked own a dog or cat. 15% do not own a pet at all. The remaining people asked were fish owners. If they polled 160 people, how many fish owners are there?

Solution

Let's break down the problem step by step.

  • Total people surveyed = 160
  • 3/4 of those asked own a dog or cat.
  • 15% do not own a pet at all.
  • The remaining people are fish owners.

Step-by-Step Calculation:

  1. People who own a dog or cat: 34\frac{3}{4} of 160: 34×160=120 people\frac{3}{4} \times 160 = 120 \text{ people}

  2. People who do not own any pets: 15% of 160: 0.15×160=24 people0.15 \times 160 = 24 \text{ people}

  3. Fish owners: The remaining people will be the fish owners. So, subtract the number of dog/cat owners and non-pet owners from the total: 16012024=16 fish owners160 - 120 - 24 = 16 \text{ fish owners}

Thus, there are 16 fish owners.

Do you need more details on any part of the solution?

Related Questions:

  1. What percentage of the people are fish owners?
  2. If the number of people increases to 200, how many would be fish owners using the same ratios?
  3. How many people would own both a dog and a cat if half of the dog/cat owners have both?
  4. What is the ratio of fish owners to non-pet owners?
  5. How many people are not fish owners?

Tip:

Always check if all percentages and fractions are accounted for when solving survey-based problems to avoid missing groups!

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Math Problem Analysis

Mathematical Concepts

Percentages
Fractions
Basic Arithmetic

Formulas

People who own a dog or cat = (3/4) * Total people
People who do not own a pet = (15/100) * Total people
Fish owners = Total people - (Dog/Cat owners + Non-pet owners)

Theorems

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Suitable Grade Level

Grades 5-7