Scenario: Paint Mixing - Use equations to solve proportional mixing problems!
To create orange paint, you need to mix red and yellow paint in a ratio of 2:3. If you have 10 liters of red paint, how much yellow paint do you need?
Problem: Red:Yellow = 2:3, Red = 10L, Yellow = ?
Step 1: Set up the proportion
Red/Yellow = 2/3
Since Red = 10L: 10/Yellow = 2/3
Step 2: Cross multiply
10 × 3 = 2 × Yellow
30 = 2 × Yellow
Step 3: Solve for Yellow
Yellow = 30 ÷ 2 = 15 liters
Step 4: Verify the ratio
10:15 = 2:3 ✓ (both ratios equal 2/3)
Answer: You need 15 liters of yellow paint.
For any proportion a/b = c/d, we can cross multiply to get: a × d = b × c
a/b = c/d
Cross multiply:
a × d = b × c
A recipe calls for 2:3 ratio of flour to sugar. If you want to use 6 cups of flour, how much sugar do you need?
Solution:
2/3 = 6/sugar
2 × sugar = 3 × 6 = 18
sugar = 18 ÷ 2 = 9 cups
Mix red and blue paint in a 3:2 ratio to make 50 liters of purple paint. How much of each color do you need?
Solution:
Let x = amount of red paint
Then blue paint = 50 - x
3/2 = x/(50-x)
3(50-x) = 2x
150 - 3x = 2x
150 = 5x
x = 30 liters red, 20 liters blue
A map scale is 1:50000. If two cities are 4 cm apart on the map, what is the actual distance?
Your solution:
A fruit punch recipe uses orange juice and apple juice in a 4:1 ratio. If you have 12 cups of orange juice, how much apple juice do you need?
Your solution: