24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?

Soln:
Let there be 4x lbs of P in X and x lbs of V in X
Let there be y lbs of P in Y and 5y lbs of V in Y

Now total P is
4x + y = 24
and total Q is
x + 5y = 25

Solving the two equations, we get
x = 5 and y = 4

Mixture X has 4x lbs of P = 4x = 4 * 5 = 20lbs

20

px/vx=4/1, py/vy=1/5,
px+py=24
vx+vy=25

px+py=24
px/4+5py=25

px+5-px/20=24 ==> px=20

Px/Vx=4/1

Py/Vy=1/5

Px=4Vx

5Py=Vy

Px+Py=24
Vx+Vy=25

Px+Py=24
Px/4+5Py=25

-5px-5Py=-120
+Px/4+5Py=25

(Px-20Px)/4=-95 --> -19Px=-380

Px=20

I dont understand the logic..seems like such a simple problem:(

don't beat yourself up so much. Most of people happen to stumble even at the easy problems (including me). I'll give you an explanation in words. Just look at the post of gmatblackbelt while you read this. Remember to look at each two lines as a pair (first and second are together, third and fourth are together, fifth and sixth are together and so on):

first two pairs represent what is stated in the problem - a proportion

second two represent what is done when outside unknowns are matched vs. inside unknows (look above)

third two mean that if you combine P coffee from x and y mixture you will get 24 (same thing for V)

This one is the key. To solve this problem you will need to replace Vx and Vy with Px and Py(because it is what you were asked to find). You just need to look at the lines above to figure out how much is it

Next line. Because you cannot solve the equation with two unkowns you need to multiply the equation above with -5

Then, you will eliminate 5py with -5py and sum up all other number and solve the equation.

It does seem complicated in the beginning but once you adjust it is fairly easy.

let me now if you need anything else with this

Also you can solve it by picking numbers. I did this way very quickly. found 20 as well.

Good question.. thanks for the good explanation.

Just curious, would you consider this easy, medium or hard GMAT level

agree with barakhaiev... picking numbers worked out quicker for me... against creating variables and equations...!

I got 20 also. Quant is not my strong point but here is how I did it.

Using the ratio of P to V in Coffee X, we find that 4/5 of Coffee X is from Coffee P. Since they P and V are mixed it is assumed that they are both used completely. So the amount of Coffee P not used in Coffee X must be equal to the amount of P used in Coffee Y. So from the ratios we get 1/5X=1/6, we solve for X to find that 5/6 of Coffee P was used in Coffee X. Multiply 5/6 by 24 to get the answer 20.

24 lbs of coffee P and 25 lbs of coffee V
make
Coffee X and Coffee Y
such that
P:V in coffee X is 4:1
P:V in coffee Y is 1:5
and
X + Y = 49

System of Equations

P1 + V1 = X (eq.1)
P2 + V2 = Y (eq.2)

P1 + P2 = 24 (eq.3)
V1 + V2 = 25 (eq.4)

P1 = (4/5)x
P2 = (1/6)y

V1 = (1/5)x
V2 = (5/6)y

===========================
From eq. 3:

(4/5)x + (1/6)y = 24
(1/6)y = 24 - (4/5)x

y = 144 - (24/5)x

(1/5)x + (5/6)y = 25

===========================

(1/5)x + (5/6)(144 - (24/5)x) = 25
(19/5)x = 95
x = 25

==========================

Y = 49 - x
Y = 24

---

P1 = (4/5)(25) = 20
P2 = (1/6)(24) = 4


[MF1415:XDJ]

I too got 20...Good Question ...

X : 4x: x
Y : y:5y


4x+y= 24
x+5y=25

x=95/19=5 but in X : 4x: x

therefore p= 20

Divide Coffee P & Coffee Y into 2 parts each

a ................. (24-a) ...... || .......... b .............. (25-b)
Coffee A ......................................... Coffee Y

Ratio in Coffee X\(= \frac{a}{b} = \frac{4}{1}\)

Ratio in Coffee Y\(= \frac{24-a}{25-b} = \frac{1}{5}\)

Solving, a = 20; b = 5

P contained in the mixture X = 20

Kindly update the OA.....

I did as below :

(1) Coffee x + Coffee y = 49
(2) (4/5)x + (1/6)y = 24

(2) 30 * [(4/5)x + (1/6)y ]= 24 * 30
24x + 5y = 720

Then,
(1) - (2)

5x+5y=245
- (24x+5y=720)
--------------------
-19x = -475
x = 25

Then,
X has (4/5) P,
25 * (4/5) = 20 in P

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