I’m trying to mix a very particular purple for an art project, and my brain keeps doing somersaults over proportions. The guide says the color I like is 2 parts red to 5 parts blue. I’ve got exactly 350 ml of blue ready to go. I did this: red/blue = 2/5, so red = (2/5) * 350 = 140 ml. That feels right, but I’m second-guessing myself because sometimes I see people use parts of the total instead, like red = (2/7) * total. Are those two ways the same here, or am I mixing metaphors with my paint? Could someone explain which interpretation is correct and why? Also, follow-up: if I accidentally glug an extra 60 ml of red into the bucket (classic me), what would be the new red:blue ratio, and is there a clean proportional way to fix it by adding more blue instead of starting over? I keep tying myself in knots about whether to scale from the part I have or the total I want.
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5 Responses
Ooh, paint ratios are my happy place! You did the right thing: with 2 parts red to 5 parts blue and 350 ml of blue, red = (2/5)·350 = 140 ml. The “parts-of-total” view says the total is 7 parts, so red is 2/7 of the total; since blue is 5/7 of the total, total = (7/5)·350 = 490 ml, and red = (2/7)·490 = 140 ml. Some folks even say “take 2/7 of the blue,” which kind of feels symmetric because 2 out of 7 parts are red-but that 2/7 actually applies to the total, not directly to the blue, so you’d be short if you tried that shortcut. For the accidental glug: you’d have 140 + 60 = 200 ml red with 350 ml blue, so the new ratio is 200:350 = 4:7. To fix it proportionally by adding blue, keep red at 200, and use the 2:5 pattern: if 2k = 200, then k = 100 and blue should be 5k = 500 ml-so add 150 ml blue. (I once did this with lemonade and kept adding sugar “by halves,” which somehow made it sweeter-oops-until I noticed the 2-to-5 scale factor trick.) Nice visual rundown on ratios here: https://www.khanacademy.org/math/arithmetic/arith-review-ratios-prop/arith-review-ratios-intro/v/basic-ratios
You’re spot on: with a 2:5 red:blue ratio and 350 ml of blue, using red = (2/5) × blue gives 140 ml of red. The “parts-of-total” way is the same idea, just rephrased: 2:5 means 2 out of 7 parts are red and 5 out of 7 are blue, so blue = (5/7) × total = 350 ⇒ total = 350 × (7/5) = 490, and then red = (2/7) × 490 = 140. Both methods agree as long as you’re consistent about what you’re scaling from. If you accidentally poured an extra 60 ml of red (been there-my first time mixing purple for a poster, I turned it into “royal grape” by overdoing the red), then red is 140 + 60 = 200 ml while blue is still 350 ml, so the new ratio is 200:350, which simplifies to 4:7. To fix it by only adding blue, use the original ratio red:blue = 2:5, so blue should be (5/2) × red = (5/2) × 200 = 500 ml. You currently have 350 ml blue, so add 150 ml more blue and you’re back to the 2:5 balance. If it helps, think “2 of 7 total parts are red” or “red is 2/5 of blue”-choose whichever anchor (total or a known part) you actually know. Nice visual walkthrough here: https://www.khanacademy.org/math/arithmetic/arith-review-ratios-prop/arith-review-ratios/v/intro-to-ratios
You’re thinking about it exactly the right way: “2 parts red to 5 parts blue” means red:blue = 2:5, so if blue is 350 ml, scale by the same factor k with red = 2k and blue = 5k; since 5k = 350, k = 70 and red = 2k = 140 ml. The “parts-of-total” view is the same idea in different clothes: there are 7 parts total, blue is 5/7 of the total, so total = 350 × (7/5) = 490 ml, and red = (2/7) × 490 = 140 ml. Both approaches are equivalent as long as you’re consistent about which quantity you start from. If you accidentally add an extra 60 ml of red, you’ll have red = 200 and blue = 350, giving a ratio 200:350, which simplifies to 4:7. To fix it by adding blue, match the target 2:5 relative to your current red: blue should be (5/2) × 200 = 500 ml, so add 150 ml of blue. Do you have a target total volume or container limit you’re aiming for, or would a “remove a bit to correct” method be more practical for you?
You’re on the right track! A ratio of 2 red to 5 blue means “for every 5 parts of blue, use 2 parts of red,” so if you already have 350 ml of blue, scaling from the part you know gives red = (2/5)×350 = 140 ml, which is exactly right. The “parts-of-total” view is the same idea, just phrased differently: there are 7 total parts, so red is 2/7 of the total and blue is 5/7 of the total-only catch is the total isn’t 350, it’s 350×(7/5) = 490 ml. If you plug 350 straight in as the total (I did that at first too!), you’d get the wrong red amount, which is why scaling from the known part feels safer here. After the accidental extra 60 ml of red (been there…), you’d have red = 200 ml and blue = 350 ml, so the new ratio is 200:350, which simplifies to 4:7. To fix it by adding only blue, keep red at 200 and make blue match the 2:5 recipe: blue should be (5/2)×200 = 500 ml, so add 150 ml more blue and you’re back at a perfect 2:5 mix. I sometimes think of it as “scale the whole recipe so that the red part lands on 200,” which is the same logic, just dressed up in words. Hope this helps!
You’re thinking about it exactly the right way: “2 parts red to 5 parts blue” means the red-to-blue ratio is 2/5, so if you already know the blue amount, you scale from the part you have. With 350 ml of blue, red = (2/5) × 350 = 140 ml. If instead you’re planning by total volume, then there are 7 parts in all, so red = (2/7) of the total and blue = (5/7) of the total. These two views are consistent: for example, if blue were 10 ml, then red would be (2/5) × 10 = 4 ml, giving 4:10 which simplifies to 2:5; and if the total were 14 ml, red would be (2/7) × 14 = 4 ml and blue 10 ml-same mix. Now, about the “oops” moment: adding 60 ml extra red makes red = 140 + 60 = 200 ml while blue stays 350 ml, so the new ratio is 200:350, which simplifies to 4:7. To fix it by only adding blue, set 200/blue = 2/5, which gives blue = 500 ml, so add 150 ml of blue; check: 200:500 reduces to 2:5. In other words, you’ve brought it back so red is 40% of the mixture-well, close enough for mixing by eye!