Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

If the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c? 4513254576

Short Answer

Expert verified
The ratio of a to c is 415.

Step by step solution

01

- Identify given ratios

The ratio of a to b is given as 4:3, which can be written as ab=43. The ratio of b to c is given as 1:5, which can be written as bc=15.
02

- Express one ratio in terms of a common variable

From bc=15, we have b=c5. We can substitute this into the first ratio to express a in terms of c.
03

- Substitute b in the first ratio

Substitute b=c5 into ab=43, giving us ac5=43.
04

- Simplify the ratio

Simplify ac5=43 by multiplying both sides by c5. This gives a=43c5=4c15.
05

- Find the ratio of a to c

Since a=4c15, the ratio of a to c is ac=4c15c=415.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ratio and Proportion
Understanding the concept of ratio and proportion is crucial to solving problems like these. In this exercise, we have two given ratios: the ratio of a to b is 4 to 3, and the ratio of b to c is 1 to 5. Ratios compare quantities relative to each other. To solve it, we express one of the ratios using a common variable.
We start by noting that the ratio of a to b can be written as ab=43. This means for every 4 units of a, there are 3 units of b. Similarly, for b to c, bc=15, showing for every 1 unit of b, there are 5 units of c. By finding a common variable and substituting effectively, we can simplify the problem.
Algebraic Manipulation
Algebraic manipulation is managing and rearranging equations to isolate variables and simplify expressions.
From the second ratio bc=15, we derive b=c5. To find the ratio of a to c, we substitute b=c5 into the first ratio. Hence, ab=43 becomes ac5=43.
Next, we simplify by multiplying both sides by c5, resulting in a=43c5=4c15. Consequently, the ratio of a to c is 415. By carefully applying these steps, the problem is methodically broken down, making the final solution precise and graspable.
Test Preparation
Proper test preparation is key to mastering problems like these. To excel, practice solving different types of ratio problems and familiarize yourself with algebraic manipulations.
Begin by reviewing core concepts regularly and employ mnemonic strategies to remember key formulas. Practice identifying and substituting common variables. Understand the process of transitioning from one ratio to another by expressing them in terms of a common variable. This will help in solving multi-step problems efficiently.
Utilize daily practice problems, mock GMAT exams, and reviewing detailed solutions to reinforce learning. Lastly, time yourself when solving these problems to improve speed and accuracy under exam conditions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free