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

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A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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17 Sep 2018, 00:50
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25% (medium)

Question Stats:

76% (01:55) correct 24% (02:10) wrong based on 51 sessions

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A paint store mixes $$\frac{3}{4}$$ pint of red paint and $$\frac{2}{3}$$ pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

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A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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17 Sep 2018, 01:10
Bunuel wrote:
A paint store mixes $$\frac{3}{4}$$ pint of red paint and $$\frac{2}{3}$$ pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

The easiest way to solve this problem is to assume the size of a pint - Let the size be 12 units.

To make a pint of Perfectly Purple,
we will need $$\frac{3}{4}$$ pint of Red paint or 9 units and $$\frac{2}{3}$$ pint of Blue paint or 8 units.

We will need $$9$$ units out of $$9+8 = 17$$ units to be red paint to make the "Perfectly Purple" color

Therefore, to make 34 pints of Perfectly Purple color, we need $$\frac{9}{17} * 34 = 18$$(Option B) pints of Red paint.
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Re: A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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17 Sep 2018, 07:12
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Bunuel wrote:
A paint store mixes $$\frac{3}{4}$$ pint of red paint and $$\frac{2}{3}$$ pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

We're told that the red and blue paints are mixed in the following ratio: red paint/blue paint = (3/4)/(2/3)
Let's first SIMPLIFY this ratio.

(3/4)/(2/3) = 3/4 x 3/2
= 9/8

So, red paint/blue paint = 9/8

So, for example, we might mix 9 pints of red paint with 8 pints of blue paint to get 17 pints of Perfectly Purple
Similarly we might mix 18 pints of red paint with 16 pints of blue paint to get 34 pints of Perfectly Purple
Voila!!

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Joined: 26 Aug 2018
Posts: 7
A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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17 Sep 2018, 13:11
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

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Re: A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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18 Sep 2018, 17:46
Bunuel wrote:
A paint store mixes $$\frac{3}{4}$$ pint of red paint and $$\frac{2}{3}$$ pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

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.

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Joined: 15 Sep 2018
Posts: 30
Re: A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of  [#permalink]

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22 Sep 2018, 01:17
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:

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

Re: A paint store mixes 3/4 pint of red paint of red paint and 2/3 pint of &nbs [#permalink] 22 Sep 2018, 01:17
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