A paint store makes peach paint according to the formula

Question

A paint store makes peach paint according to the formula above. The numbers of gallons of white and yellowpaint used in a batch of peach paint are always each an integer. If the store ownerwants to make the smallest batch of peach paint possible, how many gallons of red are needed?

A. 1/4
B. 1
C. 3 3/4
D. 5
E. 9

Show Answer

Official Answer

C

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A. 1/4
B. 1
C. 3 3/4
D. 5
E. 9

Bunuel · Accepted Answer

White: 3/5 gallon
Red: 1/4 gallon
Yellow: 1/3 gallon

The ratio of the # of gallons of white and yellow paint needed is: (3/5)/(1/3)=9/5 --> W:Y=9:5. So, the smallest batch of peach paint possible so that the # of gallons of white and yellow paint used to be an integer should have 9 gallons of white and 5 gallons of yellow paint.

Now, if we use 9 gallons of white pain then the # of gallons of red paint we should use will be: W/R=(3/5)/(1/4)=12/5 --> 9/R=12/5 --> R=45/12=3.75 gallons.

Answer: C.

m760 · Answer

Littel confusing but got 3 3/4 as ans

whats the OA ??

Abhii46 · Answer

The question is quite confusing. Can somebody explain.

boomtangboy · Answer

Seriously what does the question want ?

karun0109 · Answer

^ nice explanation. thanks.

m760 · Answer

if the White and yellow figures has to be an interger then minum litres possible = LCM of 3 , 5 = 15
with 15 (min figure) the no of litres of yellow and white would be an interger always

So no of litres of red = 15 * 1/4 = 3 3/4

Bunuel · Answer

That's not correct: the smallest batch of peach paint possible so that the # of gallons of white and yellow paint used to be an integer is 9+5+3.75=17.75 liters.

stevie1111 · Answer

Bunuel, I did not quite get your explanation here. Can you pls elaborate?

Bunuel · Answer

What exactly didn't you get?

The smallest batch of peach paint possible so that the # of gallons of white and yellow paint used to be an integer should have  9 gallons of white  and  5 gallons of yellow paint , plus  3.75 gallons of red . Total: 9+5+3.75=17.75 liters.

You can check whether this is correct: 
3/5+1/4+1/3=71/60 gallons;
Share of White: (3/5)/(71/60)=36/71;
Share of Red: (1/4)/(71/60)=15/71;
Share of Yellow: (1/3)/(71/60)=20/71;

In 17.75 liters.:
Amount of White: 36/71*17.75=9 liters;
Amount of Red: 15/71*17.75=3.75 liters;
Amount of Yellow: 20/71*17.75=5 liters.

stevie1111 · Answer

Apologies for not making my question clear. I did not understand why is the LCM method of arriving at 15 here as posted by 'm760' incorrect?

Bunuel · Answer

m760 incorrectly assumed that 15 liters of paint was the smallest batch of peach paint possible so that the # of gallons of white and yellow paint used to be an integer. Actually it's 17.75 liters.

Please read this: a-paint-store-makes-peach-paint-according-to-the-formula-129492.html#p1063197 and this: a-paint-store-makes-peach-paint-according-to-the-formula-129492.html#p1066489

Also notice that given formula (White: 3/5 gallon, Red: 1/4 gallon, Yellow: 1/3 gallon), does not give us the shares of each paint for 1 gallon of peach paint since 3/5+1/4+1/3=71/60>1. Shares would be: W:R:Y=36:15:20 --> W:Y=36:20:9:5.

Hope it's clear.

stne · Answer

I think what m760 meant was that the smallest number possible so that white and yellow are integers is 15 ( Lcm of 3 and 5 )

anything lesser than 15 will not give white and yellow as integers and the smallest number which will give white and yellow as integers is 15.

so when white and yellow are minimum integers what is red? 3/5 : 1/4 : 1/3 = 9: 15/4 : 5

so as we can see red is 3.75

no where has m760 mentioned that the smallest amount of PEACH PAINT is 15 what he meant was the smallest number by which we have to multiply white( 1/3) and yellow ( 1/5) to make these integers is 15 . so when white and yellow are smallest integers what would be the value of red , red would be 15/4 = 3.75.

I think m760 way is another valid way of doing this sum

jlgdr · Answer

Start by finding the LCM of the three numbers which is 60 Then you will have 12,15,20 Your only restriction are White and Yellow to be integers so keep reducing until you wnd up with 3:15/4:5 So C is your answer Cheers! J

Consider providing Kudos if it helps

shashankism · Answer

The formula for the peach paint is given as : 
White = 3/5 gallon
Red = 1/4 gallon
Yellow = 1/3 gallon

That means in this ratio it can be mixed always to make peach paint.

Now the question says the volume of white and yellow paint must be an integer.
So we have to take LCM of 5 and 3 to make both volumes of white and yellow paint an integer.
Minimum multiplication factor = 15
White Paint = 3/5 * 15 = 9 gallon
Yellow Paint = 1/3 * 15 = 5 gallon 
Red paint can be decimal. So red paint = 1/4 * 15 = 3 3/4 gallon.

Answer C.

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A paint store makes peach paint according to the formula

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