Jug contains water and orange juice in the ratio 5:7 . anoth

5x/12 + 7y/9 = 3/7(x+y)

solving the equation, we have x/y = 88/3.

Hi folks,

I solved this problem. However, I am not able to get where I messed up such that I am unable to reach to the solution.

J1: 5:7

J2: 7:2

J3: 3:4 (J1+J2)

Let us take x from J1 and y from J2

Water from X: 5x
Water from Y: 7y

Orange from X: 7x
Orange from Y: 2y

Given in the question is that in what ratio J1+J2 such that J3: 3:4 Implies we have to calculate x:y

=> (5x+7y)/(7x+2y) = 3/4

=> (5 (x/y) + 7)/( 7 (x/y) +2) = 3/4

=> ( 5A + 7 ) / (7A +2 ) = 3/4

=> A=22

=> (x/y) = 22

Please advice where I am committing mistake.

Thanks in advance

Rgds,
TGC !!

You need to understand what you are doing. What do you mean by 'take x from J1'? What is x? Volume in lts? Fraction of total mixture? Think about it.
Say it is volume in lts.

Then
Water from X: 5x/12 lts
Water from Y: 7y/9 lts

Orange from X: 7x/12 lts
Orange from Y: 2y/9 lts

Given that water:orange in J3 is 3:4, we get amount of water in J3 is 3(x + y)/7 lts
Amount of orange in J3 = 4(x+y)/7 lts

We get
(5x/12 + 7y/9)/(7x/12 + 2y/9) = 3/4
(45x + 84y)/(63x + 24y) = 3/4
180x + 336y = 189x + 72y
9x = 264y
x/y = 88/3

But this is an extremely convoluted way of solving this question. Check out the methods given above.

You arrive here \(x=22y\)<== this is not the end.

We know that \(5x+7x=12x\) and that \(7y+2y=9y\). X can be seen as \(12*22y=264y\) and now you have a fraction of this form \(\frac{264y}{9y}=\frac{88}{3}\).

Or method #2

\(\frac{x}{y}=22\) but x must be "taken" in groups of 12 and y in groups of 9 so \(\frac{12x}{9y}=22*\frac{12}{9}=\frac{88}{3}\)

Hope it's clear

Still remains a query for me,here is the question:

In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4 ????

X of J1 and Y of J2 to get J3 (3:4)

And X:Y = 22:1

Plz advise !

Rgds,
TGC !

Your solution is not complete.

You arrive here \(x=22y\), is correct BUT is not the end.

The solutions must be mixed in the following ways \(\frac{12x}{9y}\) (because \(5x+7x=12x\) and \(7y+2y=9y\))

A group/liter of the first solution must contain 12x, same reasoning for the second that must contain 9y.

\(\frac{x}{y}=22\) but x must be "taken" in groups of 12 and y in groups of 9 so \(\frac{12x}{9y}=22*\frac{12}{9}=\frac{88}{3}\).

x/y is not what we are looking for : \(\frac{12x}{9y}=?\)<===this is the question, and \(\frac{x}{y}\) does not answer it.

Hope I've explained myself well.

Still on the same page , I got the answer 22 after a year following my instinct.

W:O
5:7 X
7:2 Y
3:4

{5X+7Y}/{7X+2Y} = 3/4

X/Y =22

Reasoning:

Take X from Sol1 and take Y from Sol2

The question is "In what proportion should these 2 liquids be mixed to give a water and orange juice in ratio 3 : 4"

And not "In what proportion should water and orange be mixed"

Please advise

I think I can see were you went wrong.

From your solution:
The volume of jug 1 = x liters. The ratio of water to orange there is 5:7;
The volume of jug 2 = y liters. The ratio of water to orange there is 7:2;

Then you want to make the ratio of water to orange in the mixture so that it will be 3 to 4. In your solution: (water)/(orange) = (5X+7Y)/(7X+2Y) = 3/4.

But, the amount of water in jug 1 is NOT 5x, it's 5/12*x and the amount of water in jug 2 is NOT 7y, it's 7/9*y.

Similarly the amount of orange in jug 1 is NOT 7x, it's 7/12*x and the amount of orange in jug 2 is NOT 2y, it's 2/9*y.

Hence the equation should be: \(\frac{\frac{5}{12}x+\frac{7}{9}y}{\frac{7}{12}x+\frac{2}{9}y}=\frac{3}{4}\) --> \(\frac{x}{y}=\frac{88}{3}\).

Answer: C.

Does this make sense?

But, the amount of water in jug 1 is NOT 5x, it's 5/12*x and the amount of water in jug 2 is NOT 7y, it's 7/9*y.

I disagree with the above statement since if we want to know the actual quantity of the ingredient in the solution we multiply it by common factor, here taken as x.

So,

x is taken as common multiplying factor from first solution and so do y is taken for another solution.

So when we mix them resulting has a 3:4.

(5X+7Y)/(7X+2Y) = 3/4

Please suggest

What is x in your equation? If it is the amount of liquid in jag 1, then the amount of water in it is 5/12*x. For example, if the amount of liquid in jag 1 is 12 liters then the amount of water is 5/12*12=5 liters and amount of orange is 7/12*12=7 liters.

Consider below:

Water:oil = 3:4.......(1)

Water : oil = 5:3..........(2)

We have to make a mixture of water:oil = 4:5

I take x ltr from (1) and y ltr from (2)

So what is the quantity of water in new solution 3x+5y

What is quantity of oil in the new solution 4x+3y

What should be the new ratio for the given values of (x,y)? 4:5

(3x+5y)/(4x+3y) = 4/5

Please tell where I am going wrong?

Water:oil = 3:4.

If you take x liters from this mixture, there will be 3/7*x liters of water there. For example, if you take 7 liters of that mixture there will be 3/7*7=3 liters of water and 4/7*7=4 liters of oil there

Sorry cannot explain any better...

Water: Oil = 3:4

When we deal with ratios, we consider a common multiplier to have absolute value of that quantity in a mixture.

I think I got my mistake.

Scenario 1:

When I want to get absolute value of the quantity in the mixture , I multiply by the factor X.

water is 3X and Oil is 4X in the mixture.

Scenario 2:

When I take X of this mixture then the water content contributed by this X ltrs from this mixture is

Water/Total * X = 3/7*X in this case

Thanks !

Well this was a too silly doubt to answer.

Rgds,
TGC!

1. (Quantity of jug 1)* proportion of water + (Quantity of jug 2)* proportion of water / (Quantity of jug 1)* proportion of juice + (Quantity of jug 2)* proportion of juice = 3/4
2. Let x and y be the quantities in jug 1 and jug 2 resp to get the mixture
3. (x*5/12 + y*7/9) / (x*7/12 + y*2/9) = 3/4
x/y=88/3

Can this be solved using alligations?

Just take one of them. I took water to solve it.

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