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51 cars in the parking lot











































Ratio of white cars

There are 51 cars in the parking lot, of which 11 are white. Write a ratio of white cars to cars that are not white.

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Dec 18, 2012
Ratio
by: Staff


Answer


Part I

Math – 51 cars in parking lot:  40 non-white cars, 11 white cars




There are 51 cars in the parking lot, of which 11 are white. Write a ratio of white cars to cars that are not white.


Calculate the number of non-white cars

(non-white cars) + (white cars) = (Total number of cars)

(non-white cars) + 11 = 51

(non-white cars) = 51 - 11

(non-white cars) = 40


Parking lot Parked Car Summary

Non-White Cars = 40

White Cars = 11

Total number of cars = 51


What is the ratio of white to non-white cars?
Ratio (white to non-white cars) = (white cars):(non-white cars)


Ratio (white to non-white cars) = 11:40

number white cars
Ratio (white to non-white cars) = --------------------------
number of non-white cars

11
Ratio (white to non-white cars) = -------
40

Ratio (white to non-white cars) = 0.275


The final answer is: Ratio (white to non-white cars) = 0.275



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Dec 18, 2012
Ratio
by: Staff

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Part II


You may be asking yourself why ratios are important:

Why not just use the numerical total for the number of white and non-white cars? 11 white cars and 40 non-white cars. That is straightforward and easy to understand.

This is why:

Ratios are a CONVENIENT WAY to EXPRESS a PROPORTION.

Calculating a ratio may seem like unimportant and unnecessary work. However, once the a ratio is known, it is easy to apply that ratio to math problems involving direct proportions.

RATIOS are EASY TO UNDERSTAND

For example, suppose two students have the following academic averages: 84% and 86%. These are actually the ratios 0.84 and 0.86.

It is easy to see that (all other things being equal) the student with the 0.86 ratio average is the better student. All anyone has to do is look at the numbers. 0.86 is a bigger number than 0.84. 0.86 is better than 0.84.

Even if the person reading the two numbers (0.84 & 0.86) has no idea how a ratio is calculated, they still understand that 0.86 is bigger and better than 0.84.



What ratios actually mean:

I will continue to use the example of the two students who earned the 84% and 86% averages (ratios of 0.84 and 0.86).

For this example, the students earned their percentage scores entirely from multiple choice tests.

(Students in the real world do more than just take multiple choice tests. However, for this example that’s all they do.)

A ratio of 0.84 means that for every 100 multiple choice questions this student attempted to answer, this student answered 84 correctly.

A ratio of 0.86 means that for every 100 multiple choice questions this student attempted to answer, this student answered 86 correctly.

By now you are probably thinking: Students’ are not given tests with exactly 100 questions every time. What about a student that is given a test with only 75 questions, or the student who is given a test with 150 questions?

A ratio calculation compensates for these differences. That is one reason a ratio is so practical.

However, the most STRAIGHTFORWARD way to represent a PROPORTION is to USE a FRACTION.



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Dec 18, 2012
Ratio
by: Staff


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Part III

For example, suppose the first student in the example actually took a test with only 75 questions and answered 63 questions correctly.

The proportion of questions answered correctly can be represented by the fraction 63/75 (63 correct answers out of 75 questions).

Now suppose the second student in the example actually took a test with 150 questions and answered 129 questions correctly.

The proportion of questions answered correctly can be represented by the fraction 129/150 (129 correct answers out of 150 questions).

Which student is the best student?

Compare the fractions.

Which student has the highest average (which is the larger fraction)? 63/75 or 129/150?

It may be hard to answer that question by merely glancing at these fractions.

Writing fractions to represent a proportion may be easy, but comparing different fractions can be frustrating and time consuming.


Using a ratio to compare two proportions does not have this difficulty.

Comparing two ratios is easy to do. That is one of the reasons a ratio is often used instead of a fraction.


(However, remember that a fraction and a ratio both REPRESENT exactly the same thing: a PROPORTION.)


RATIOS are EASY TO USE

Ratios are used in many types of calculations.

For example, suppose the government imposes an 8% sales tax on the items you purchase. That is a ratio of 0.08. This means that for every dollar you spend, you owe an additional 8 cents in sales tax.

It is easier to express the tax as a ratio because different people spend different amounts of money. The tax on different amounts of money will be different.

Suppose person “A” spends $51. How much sales tax do they owe?

Calculation of Sales Tax for person “A”: $51 * .08 = $4.08

Suppose person “B” spends $16. How much sales tax do they owe?

Calculation of Sales Tax for person “B”: $16 * .08 = $1.28






Thanks for writing.

Staff
www.solving-math-problems.com


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