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Green paint is made by mixing blue paint with yellow paint in a ratio 29 Oct 2020, 10:28
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Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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Green paint is made by mixing blue paint with yellow paint in a ratio 29 Oct 2020, 13:27
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Sajjad1994
Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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Ratio of Green and Blue in Turquoise paint = y : 2

Amount of green paint in 10 gallons of Turquoise paint = \(\frac{y}{y + 2} * 10\)

Ratio of Blue and Yellow in Green paint = 2 : x

Amount of Yellow paint in \(\frac{10y}{y + 2}\) gallons of Green paint = \(\frac{x}{x + 2} * \frac{10y}{y + 2} = \\
\frac{10xy}{(x + 2) \space (y + 2)}\)


Option A

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Green paint is made by mixing blue paint with yellow paint in a ratio 29 Oct 2020, 13:51
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Assume y=3, since (3+2 is a factor of 10)

Green paint required = 3/5 * 10 = 6L

Assume x=1, since (1+2 is a factor of 6)

Yellow paint required = 1/3 * 6 = 2L

Put x=1 and y=3 for each option.

Option A - \(\frac{30}{3*5 }= 2\) (What we want)

Option B- \(\frac{30}{5*5} ≠ 2\)

Option C- \(\frac{20}{5} ≠ 2\)

Option D- \(\frac{30}{5} ≠2\)

Option E doesn't make any sense to me


A




Sajjad1994
Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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Green paint is made by mixing blue paint with yellow paint in a ratio 05 Nov 2020, 12:32
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Sajjad1994
Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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Solution:

It is easier to solve this problem by using numbers.

If blue paint is 2 gallons and yellow paint is x = 6 gallons, then green paint is 2 + 6 = 8 gallons. If green paint is y = 8 gallons and blue paint is 2 gallons, then turquoise paint is 10 gallons. We see that if x = 6 and y = 8, then 6 gallons of yellow paint are needed to make 10 gallons of turquoise paint.

Now, let’s see which answer choices will yield the value of 6 when x = 6 and y = 8:

A) 10(6)(8)/[(6 + 2)(8 + 2)] = 480/80 = 6

B) 10(6)(8)/[(6 + 4)(8 + 2)] = 480/100 = 4.8

C) 20(6)/(8 + 2) = 120/10 = 12
D) 10(6 + 2)/(8 + 2) = 80/10 = 8

We see that only choice A yields the value of 6; thus, choice A is the correct answer.

Answer: A
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Green paint is made by mixing blue paint with yellow paint in a ratio 05 Nov 2020, 15:06
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Sajjad1994
Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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Green paint has a ratio of \(Blue:Yellow = 2:x\). By mixing 2 blue and x yellow we have x + 2 total, which means the ratio of Green : Blue : Yellow is \((x + 2):2:x\). Similarly, \(Turquoise:Green:Blue = (y+2):y:2\).

Now we need 10 Turquoise paint, to get 10 on the Turquoise side, first divide by (y+2) then mulitiply the ratio by 10. Hence multiply the entire ratio by \(\frac{10}{y+2}\) to get \(\frac{10y}{y+2}\) green. Next the ratio of Green:Yellow is (x+2):x, to get yellow from green we need \(Green*\frac{Yellow}{Green}\)so multiply \(\frac{10y}{y+2}\) green by Yellow/Green which is \(\frac{x}{x+2}\).

This results in x + 2 on the bottom, only choice A has that portion so the answer is A.

Ans: A
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Green paint is made by mixing blue paint with yellow paint in a ratio 06 May 2021, 09:19
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Goal in most ratio questions is to find the unknown multiplier to bring the values in Ratio/Relative Units to the Actual Values


Turquoise Paint Ratio

Blue : Green : TOTAL
________________
2(m) : Y(m) : (2 + Y)m

The TOTAL Actual Value of Turquoise paint needed = 10 gal

(2 + Y)m = 10

m = ratio multiplier = 10 / (Y + 2)

Actual Green Paint needed = Y(m) = Y * 10 / (Y + 2)


Green Paint Ratio:

yellow : blue : TOTAL
________________
X(n) : 2(n) : (X + 2)n


Now we need to find the ratio multiplier or n for the green paint ——-> set the Actual value of Green Paint needed from above = (X + 2)n


(X + 2)n = 10Y / (Y + 2)

n = 10Y / (Y + 2) (X + 2)

The Actual Value of Yellow Painted needed is = X (n)

Substitute in the ratio multiplier or n to get the actual value of Yellow paint:

X (n) =

X* 10Y / (Y + 2) (X + 2)

This is answer choice A

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Green paint is made by mixing blue paint with yellow paint in a ratio 25 Jun 2021, 00:00
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Green paint is made by mixing blue paint with yellow paint in a ratio of 2 to x. Turquoise paint is made by mixing green paint with blue paint in a ratio of y to 2. In terms of x and y, how many gallons of yellow paint are required to make 10 gallons of turquoise paint?

(A) \(\frac{10xy}{(x+2)(y+2)}\)

(B) \(\frac{10xy}{(x+4)(y+2)}\)

(C) \(\frac{20x}{y+2}\)

(D) \(\frac{10(x+2)}{y+2}\)

(E) \(\frac{x}{y} = \frac{2}{3}\)
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GP = green paint
BP = blue paint
TP = turquoise paint
YP = yellow paint

Let there be (2+x) units of GP.
So GP contains 2 BP and x YP

In 1 unit of GP,there will be
\(\frac{2}{(2+x)}\) BP and \(\frac{x}{(2+x)}\) YP.................................1

Let there be (2+y) units of TP
So TP contains 2 BP and y GP.

In 1 unit of TP,there will be \(\frac{y}{(2+y)}\) GP

So in 10 units of TP,there will be \(\frac{10y}{(2+y)}\) GP

Since in 1 unit of GP there is
\(\frac{x}{(2+x)}\) YP...................FROM 1


So in \(\frac{10y}{(2+y)}\) units of GP

there will be \(\frac{10xy}{(x+2)(y+2)}\) YP
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Green paint is made by mixing blue paint with yellow paint in a ratio 05 Oct 2024, 23:16
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Opinion please

Do people really find this easier to solve using test numbers assuming values for y and x? I find equations to be faster. Its like you to assume and then test each of the 5 answer choices, which is sure to take up time?
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Green paint is made by mixing blue paint with yellow paint in a ratio 11 Nov 2025, 11:37
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