i have a gallon of paint that contains 35% solids and 65% water.if i add 5% 6.4 more ounces of water to it what will the solids content be.can you show to figure this out thank you
To figure this out, first, we need to determine the initial amount of paint in the gallon and the subsequent amount of water that will be added.
Given that the gallon of paint contains 35% solids and 65% water, we can calculate the amount of solids in the gallon using the following steps:
Step 1: Calculate the total amount of paint in the gallon:
Total amount of paint = 1 gallon = 128 fluid ounces
Step 2: Calculate the amount of solids in the gallon of paint:
Amount of solids = Percentage of solids × Total amount of paint
Amount of solids = 35% × 128 fluid ounces
Now, let's calculate the amount of water that will be added to the gallon:
Step 3: Calculate the amount of water to be added:
Amount of water to be added = Percentage of water to be added × Total amount of paint
Amount of water to be added = 5% × 128 fluid ounces = 0.05 × 128 fluid ounces
Step 4: Calculate the new total amount of water in the gallon:
New total amount of water = Initial amount of water + Amount of water to be added
New total amount of water = 65% × 128 fluid ounces + 0.05 × 128 fluid ounces
Finally, we can calculate the new solids content in the gallon of paint. Since the amount of solids remains unchanged and the total amount of paint increases, the new solids content can be calculated using the following formula:
New solids content = Amount of solids / (Amount of solids + New total amount of water)
Let's plug in the values and calculate the new solids content:
New solids content = (35% × 128 fluid ounces) / ((35% × 128 fluid ounces) + (65% × 128 fluid ounces + 0.05 × 128 fluid ounces))
Simplifying the equation, we get:
New solids content = (0.35 × 128) / (0.35 × 128 + 0.65 × 128 + 0.05 × 128)
Calculating further, we have:
New solids content = (44.8) / (44.8 + 83.2 + 6.4)
New solids content = 44.8 / 134.4
Finally, we can calculate:
New solids content = 0.33333 = 33.33%
Therefore, after adding 6.4 ounces of water to the gallon of paint, the new solids content would be approximately 33.33%.