Green paint is made by mixing blue paint with yellow paint in a ratio

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

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

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

Posted from my mobile device

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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