Question

One canned orange juice is 25% orange juice another is 5% orange juice. How many liters of each should be mixed together in order to get 20 L that is 8% orange juice

Answer 1

`X = (1.6 - 0.05Y)/(0.25)= 6.4 -0.2 Y` (3)

Replcaing equation (3) into equation (2) we got:

`0.75(6.4 -0.2 Y) +0.95 Y = 18.4`

And solving for Y we got:

`4.8 -0.15 Y +0.95 Y = 18.4`

`0.8 Y = 13.6`

`Y = 17`

And solving for X from equation (3) we got:

`X= 6.4 -0.2*17 = 3`

So we need 3L of orange juice with 25% of concentration and 17 L of orange juice with 5% of concentration

Explanation:

For this problem we can work with the concentration of water and orange juice.

Let X the amount for the orange juice with 25% content and Y the amount for the orange juice with 5% of content

Using the concentration of orange juice we have:

`0.25 X + 0.05 Y = 20*0.08` (1)

And for the water we have:

`0.75 X + 0.95Y = 20*0.92` (2)

If we solve for X from equation (1) we got:

`X = (1.6 - 0.05Y)/(0.25)= 6.4 -0.2 Y` (3)

Replcaing equation (3) into equation (2) we got:

`0.75(6.4 -0.2 Y) +0.95 Y = 18.4`

And solving for Y we got:

`4.8 -0.15 Y +0.95 Y = 18.4`

`0.8 Y = 13.6`

`Y = 17`

And solving for X from equation (3) we got:

`X= 6.4 -0.2*17 = 3`

So we need 3L of orange juice with 25% of concentration and 17 L of orange juice with 5% of concentration