A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of

Red = 3/4 pint, Blue = 2/3 pint

Red + Blue = (9+8)/12 = 17/12 of Perfect Purple

How many Red + Blue we need to make 34 pints? 34/(17/12) = 24

So 24 * 3/4 (red) = 18

Answer B

Let x be the number of 3/4 pint of red paint and the number of 2/3 pint of blue paint needed to make the 34 pints of Perfectly Purple paint. We can create the equation:

(3/4)x + (2/3)x = 34

Multiplying by 12, we have:

9x + 8x = 408

17x = 408

x = 24

Thus, we would need 24 x 3/4 = 18 pints of red paint.

Alternate Solution:

We note that 3/4 + 2/3 = 17/12 pints of Perfectly Purple paint contains 3/4 pints of red paint. If we let x = the amount of red paint in 34 pints of Perfectly Purple paint, we can create a proportion and solve for x:

(3/4)/(17/12) = x/34

(3/4)*(12/17)*34 = x

x = 3 * 3 * 2 = 18

So, there are 18 pints of red paint in 34 pints of Perfectly Purple paint.

Answer: B

The total mixture (Perfectly Purple) will be given by the addition of red and blue paints:

\(\frac{3}{4}\ pint \ of\ red+\frac{2}{3}\ pint\ of\ blue=\frac{9}{12}+\frac{8}{12}=\frac{17}{12} \ pints \ of \ Perfect \ Purple\)

For 34 pints of Perfectly Purple, the number of red paint pints needed would be given by:

\(Red \ Pints=34 \ Perfectly \ purple \ pints \times \frac{\frac{3}{4}\ red\ pints}{\frac{17}{12}\ Perfectly\ Purple\ Pints} = 34 \times \frac{9}{17}=18\ pints\)

The final answer is .

simplest way possible:

1 unit of Perfectly Purple: 3/4+ 2/3==>> 9/8, which is nothing but red/blue.

Red paint's share: 9/(9+8) *34= 18