May I know why when I use the equation 3/4R+2/3B=1 (i.e. 3/4 red plus 2/3 blue to make one pint of purple) and solve simultaneously with R+B=34, I get a different answer?

\(\frac{3}{4}R+\frac{2}{3}B=1\). This equation is incorrect. 1 pint cannot contain \(\frac{3}{4}\) Red and \(\frac{2}{3}\) Blue.

The correct equation is:

\(\frac{3}{4}R + \frac{2}{3}B = \frac{17}{12}\)

or \(9R + 8B=17\) multiplying 12 on both sides.

Sometimes, ratio problems can be solved using not just part to part ratios, but part to whole ratios ( see mathisfun ratios section https://www.mathsisfun.com/numbers/ratio.html)

In this case, we are given 3/4 pint red to 2/3 pint blue. We add them together to get a whole. Like if we had 3 cats and 2 dogs, the "whole" would be 5 dogs and cats.

So, if we add the 3/4 pint red to 2/4 pint blue we get 17/12 pints of the "whole" mixture.

So, our ratio of part to whole, if we use just red as a part is 3/4 red to 17/12 whole.

We can also think of this as a conversion problem.

We are given 34 pints of a whole mixture (desired result) we can convert that quantity to red pints using our ratio of red parts to whole parts.

We can convert those whole pints to red pints by multiplying by the ratio of red pints to whole pints [ 3/4 pints red/(17/12 whole) ]

the "whole" or purple units cancel leaving the "red" units

3/4 is about 75% of red paint. Which means for every perfectly purple created you used 75% of the red paint, remaining 25%. To make 34 pints, you cannot use more than 34 pints of red paint because the remaining 25% will keep accumulating. So cancel out C - E. A is too low, so the only answer is B

we have 3/4 of pint red and 2/3 blue pint.
Asking how many red pints to make 34 pint of Perfect Purple?
3/4+2/3 = 1.41666
Red pint = (34/1.41666)*3/4= 18
B is the answer.

Here can we solve considering the LCM of 3 and 4 as 12 ?
I used this method consider 12 pint of red and blue and got the answer as 17 PINT of Purple Painting with 9 parts of red and 8 parts blue . Which means for 34 Pint of Purple painting we would require 18 parts of Red .Is this a right method?

correct

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