Math Problem Statement

A mayor wants to know how many people in her town drive certain types of vehicles. She records 50 types of vehicles as they pass the busiest intersection in town. The table shows the results.

Type of Vehicle

Number of Vehicles

Gas

34

Hybrid

5

Electric

8

Diesel

3

How many electric vehicles can the mayor expect out of 4,000 vehicles in the town?

_____ electric vehicles

Solution

To solve this, we can use a proportion based on the data recorded by the mayor.

The proportion of electric vehicles is calculated by dividing the number of electric vehicles by the total number of vehicles observed:

Proportion of electric vehicles=850=0.16\text{Proportion of electric vehicles} = \frac{8}{50} = 0.16

Now, we can apply this proportion to the total number of vehicles in the town (4,000 vehicles):

Expected number of electric vehicles=0.16×4000=640\text{Expected number of electric vehicles} = 0.16 \times 4000 = 640

Thus, the mayor can expect 640 electric vehicles out of 4,000 vehicles in the town.

Would you like further clarification or details? Here are five related questions for deeper understanding:

  1. What percentage of the vehicles in town are expected to be hybrid?
  2. How many gas vehicles are expected in the town?
  3. What is the expected number of diesel vehicles out of 4,000?
  4. How could the proportion of electric vehicles change if more were purchased over time?
  5. How would the result differ if the mayor observed 100 vehicles instead of 50?

Tip: Always ensure that proportions are correctly calculated from representative data to estimate larger populations effectively.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Proportions
Ratios
Multiplication

Formulas

Proportion of electric vehicles = (Number of electric vehicles observed) / (Total vehicles observed)
Expected electric vehicles = Proportion of electric vehicles * Total vehicles in town

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 5-7