00:01
This problem says in order to make a specific shade of green paint, a painter mixes one and one half quarts of blue paint, two cups of green paint and one half gallon of white paint.
00:08
How much of each color is needed to make 100 cups of this shade of green paint? the problem with this to start is that we don't know how much this original mixture of paint is, and we're given all the measurements of each ingredient to make the certain shade, but they're all in different measurements.
00:24
And the only one we want to leave in its original form is the two cups of green, but we want to change quartz and gallons to be a certain shade.
00:30
Cups as well so we can kind of relate this to the 100 cups that we want and we know that there's four cups for every quart so if we have one and one half quarts that's going to be six cups of the blue and like we said we want to leave the two cups of green alone because it's already in cup form and then there are 16 cups in a gallon so half of a gallon would give us eight cups so in this original mixture the total cups would be six plus two plus eight which is 16 cups what we want is the 16 cups to become 100 cups.
01:02
So we're multiplying our total of 16 by some value to make it 100.
01:06
If we can figure out what that value is to multiply 16 by to make it 100, we can multiply all of our original values by that same scale value to figure out the new measurements to make 100 cups instead of the 16 cups from the original.
01:19
So when we divide by 16, 100 over 16 doesn't divide factor that we need to apply to all of our original values.
01:32
So since they gave us our measurements in quartz cups and gallons, we'll keep them the same for our final answer.
01:38
So one in one quarts of blue has to be multiplied by 25 fourths...