Question 24. A painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint. However, by mistake, he used 3 liters of blue and 2 liters of yellow, so that he made the wrong shade of green. What is the smallest amount of this green paint that he must throw away, so that using the rest of his green paint and some extra blue and or yellow paint, he could make 5 liters of paint of the correct shade of green? To start off with, we should recognize that 1 liter is equal to 1000 milliliters. To simplify this problem, I've converted all of the answers into milliliters, like so. Now, our goal is 2 blue to 3 yellow as a ratio, so we can draw our bucket and fill it with green paint. We know that there are 5000 milliliters of green paint, 3000 milliliters of blue, and 2000 milliliters of yellow making this green paint. Now, we are trying to find the smallest amount of paint to throw away, so let's start off with our smallest possibility, 555 milliliters. If we remove 5555 milliliters, we are left with 4445 milliliters of green, but the ratio stays the same, since we did not change it. It has to stay 3 to 2, and it will look like so. 2667 milliliters of blue paint and 1778 milliliters of yellow paint. We can add in 555 milliliters of yellow paint, and when we do this, we have 2333 milliliters of yellow paint. Unfortunately, this does not give us our ratio of 2 blue to 3 yellow, so this will not be the answer. Next, we look at 600 milliliters. This leaves us with 4400 milliliters of green, and keeping the ratio of 3 to 2, we have 2640 milliliters of blue and 1760 milliliters of yellow. Adding 600 milliliters of yellow, we get 2360 milliliters of yellow. Again, 2640 blue to 2360 of yellow is not the 2 blue to 3 yellow ratio, so this is not the answer. Next up, we do 666 milliliters. Again, keeping the ratio, I think it is important here to let you know that I took my liberty with rounding a little bit. This is not exactly, but the decimal is not relevant in this question, since it will still give us the approximate answer. If we add the 666 yellow, we get 2399 milliliters of yellow. We are getting closer to our ratio, but still, this is not it. Next, we have a drastic shift. We throw away 1500 milliliters, and this is our ratio. Adding 1500 milliliters of yellow, we get 2900 milliliters of yellow paint. This is very close to our 2 to 3 ratio, but not quite there yet. Finally, when we take away 1666 milliliters of paint, our ratio looks like so. And when we add 1666 milliliters of yellow, again, since I'm rounding here, it's not an exact value. In theory, this is, in fact, 3000 milliliters of yellow paint. And this shows us 2000 milliliters of blue paint to 3000 milliliters of yellow paint. So the answer will be A, 5 thirds of a liter.

paint mixing

blue and yellow paint

correcting paint ratio

green paint recipe

paint discard