Calculate the ratio of water to plaster in a mixing formula | Step-by-Step Solution
Problem
Plaster mixing ratio calculation: 15 liters (15 kg) of water per 25 kg of plaster. Formula: w = 15/25 c = 3/5 c = 0.6 c, where w is water and c is plaster. Goal is to compute water-to-plaster ratio.
🎯 What You'll Learn
- Understand how to convert between different unit representations
- Practice calculating proportional relationships
- Apply mathematical reasoning to practical problem-solving
Prerequisites: basic division, fraction simplification, unit ratios
💡 Quick Summary
I can see you're working with a ratio problem involving a mixing formula - this is all about understanding proportional relationships! When you have 15 kg of water and 25 kg of plaster, what do you think the first step would be to express this as a simple ratio? Think about what ratios really represent - they're like recipes that show how much of one ingredient you need compared to another. Have you considered whether these numbers (15 and 25) can be simplified by finding what they have in common? I'd encourage you to start by writing out the basic water-to-plaster relationship and then see if you can reduce it to its simplest form - you've got all the information you need right there in the problem!
Step-by-Step Explanation
1. What We're Solving:
We need to find the water-to-plaster ratio for a plaster mixture that uses 15 liters (15 kg) of water for every 25 kg of plaster.2. The Approach:
A ratio compares two quantities by showing how much of one thing we have relative to another. Think of it like a recipe - we want to know "for every X amount of plaster, how much water do we need?" This helps us scale the recipe up or down while keeping the mixture consistent!3. Step-by-Step Solution:
Step 1: Identify what we're comparing
- Water: 15 kg
- Plaster: 25 kg
- We want: Water-to-plaster ratio (water : plaster)
Step 3: Simplify the ratio To make this easier to work with, let's find the greatest common factor:
- 15 = 3 × 5
- 25 = 5 × 5
- Greatest common factor = 5
So our simplified ratio is 3 : 5
Step 4: Express as a decimal (like in your formula) As a decimal: 3 ÷ 5 = 0.6 This means for every 1 kg of plaster, we need 0.6 kg of water.
4. The Answer:
The water-to-plaster ratio is 3:5 (or 0.6 when expressed as a decimal coefficient).This matches your formula w = 0.6c, where for every unit of plaster (c), you need 0.6 units of water (w)!
5. Memory Tip:
Think "3-2-5" - we need 3 parts water for every 5 parts plaster, and the difference is 2. Or remember that 0.6 is just 3/5 as a decimal - more than half a unit of water for each unit of plaster!Great job working through this - you had the right formula, and now you understand exactly where those numbers come from! 🌟
⚠️ Common Mistakes to Avoid
- Incorrectly converting between decimal and fraction representations
- Misunderstanding the relationship between water and plaster quantities
- Failing to simplify the ratio to its most reduced form
This explanation was generated by AI. While we work hard to be accurate, mistakes can happen! Always double-check important answers with your teacher or textbook.
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📷 Problem detected:
Solve: 2x + 5 = 13
Step 1:
Subtract 5 from both sides...
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