Using a Constant Factor to Solve Ratio Problems
Using a constant factor solves ratio problems by finding the multiplier that scales a simplified ratio to real-world quantities. In Grade 6 Saxon Math Course 1, students divide a known actual count by its ratio number: Actual ÷ Ratio = Constant Factor. If red to blue marbles is 4:5 and there are 36 red, the constant factor is 36 ÷ 4 = 9, so blue = 5 × 9 = 45. This method avoids cross-multiplication and works for any ratio problem where one part and its actual count are known.
Key Concepts
New Concept Ratio numbers and actual counts are related by a constant factor . $$ \operatorname{Ratio} \times \operatorname{constant factor} = \operatorname{actual count} $$.
What’s next Next, you'll use a ratio box to find this constant factor and solve problems involving everything from paint mixtures to garden weeds.
Common Questions
What is a constant factor in a ratio problem?
The number you multiply each ratio part by to find the actual count. Formula: Actual Count ÷ Ratio Number = Constant Factor.
Boys to girls ratio is 3:4 and there are 21 boys. How many girls?
Constant factor = 21 ÷ 3 = 7. Girls = 4 × 7 = 28.
How do you use constant factor when only the total is given?
Sum the ratio parts, divide the total by that sum to get the constant factor, then multiply each part by the factor.
Does the constant factor work with three-part ratios?
Yes. Find the constant factor from any known part and its actual count, then multiply all other ratio parts by that same factor.
What makes this different from setting up a proportion?
Both give the same answer, but the constant factor method is faster when you already know one ratio part and its actual value — one division and one multiplication instead of cross-multiplying.