Mixture of milk

[rohit_gmat]

Three grades of milk: 1%, 2%, and 3% fat by volume. x gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?
a. y + 3z
b. (y + z)/4
c. 2y + 3z
d. 3y + z
e. 3y + 4z


totally lost plz help.
can this solved by plugging in numbers? how do we pick numbers for this one?

[Anurag@Gurome]

Three grades of milk: 1%, 2%, and 3% fat by volume. x gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?

Form the question we can write the following equation,
--> 1*x + 2*y + 3*z = 1.5*(x + y + z)
--> x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5x = 0.5y + 1.5z
--> x = y + 3z

The correct answer is A.

[rohit_gmat]

thanks !! the algebraic way looks much clearer...!!!
is there any way to solve this with plugging in numbers?

[shankar.ashwin]

You could substitute numbers as well. Notice the resultant is between 1 and 2. So mixing an equal amount of 1% and 2% milk would yield an 1.5% milk.

Hence substitute
X=1
Y=1
Z=0.

You can see X=Y here and Z is 0.

From the answer choices you can see only A satisfies this. X=Y+3Z -> X=Y + 3(0)

[neelgandham]

GMAT Prep question isn't it ?

(1/100)*x + (2/100)*y + (3/100)*z = (1.5/100)*(x+y+z)

=> x = y + 3z

@Anurag - Is there another way(other than algebra/substitution) of solving this? like say using ratios ?

[GMATGuruNY]

I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html

[neelgandham]

I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html

Thanks GMATGuru - Is there another way(other than algebra/substitution) of solving this? like say using ratios ? The solution provided by you is more of a substitution method, isn't it?

[GMATGuruNY]

I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html

Thanks GMATGuru - Is there another way(other than algebra/substitution) of solving this? like say using ratios ? The solution provided by you is more of a substitution method, isn't it?

More than one ratio will yield the desired mixture. Check my post at the bottom of the following thread:

https://www.beatthegmat.com/allegation-t69552.html

To solve a mixture problem with 3 ingredients, I would use algebra or plug in numbers.