A decorator mixes white paint and blue paint in a ratio by volume to create a custom shade. If exactly gallons of the custom paint are needed, how many gallons of blue paint should the decorator use?
For ratio mixture questions, first add the ratio parts to find the total number of equal parts. Then identify how many of those parts correspond to the quantity you care about (here, blue paint) and form a fraction (desired parts / total parts). Finally, multiply this fraction by the total amount given (here, 6 gallons). This “total parts and fraction” method is faster and less error-prone than guessing or setting up more complicated equations.
Hints
Count total parts in the ratio
The ratio shows 3 parts white paint and 2 parts blue paint. How many parts is that altogether?
Think in terms of fractions
Once you know the total number of parts, what fraction of the mixture is blue paint?
Use the total gallons
Take the fraction of the mixture that is blue and multiply it by the total 6 gallons to find the number of gallons of blue paint.
Desmos Guide
Compute the blue paint directly
In Desmos, type: 6 * (2 / (3 + 2)). The numerical result shown is the number of gallons of blue paint needed.
Step-by-step Explanation
Interpret the ratio
The ratio (white:blue) tells you how many equal "parts" of each color are in the mixture.
- White paint: 3 parts
- Blue paint: 2 parts
So, the total mixture is equal parts.
Find the fraction that is blue
Out of the 5 total parts, 2 parts are blue.
So the fraction of the mixture that is blue is
This means of the total 6 gallons must be blue paint.
Apply the fraction to 6 gallons
Now multiply the total amount (6 gallons) by the blue fraction :
So, the decorator should use 2.4 gallons of blue paint.