Question

How would i do this??:: Some kinds of fruit juice are only 10% juice. Other brands are 40% juice how much of each kind of juice should be mixed together to form 5 gallons of punch which is 25% juice?

Answer 1

You should mix

2.5 gallons of the first juice with

2.5 gallons of the second juice

Explanation:

Step one

Let the first kind of juice be x

Let the second be y

Given x contain 10% juice

and y contains 40% juice

So for the percentage constituent concentration of each the expression is

0.1x+ 0.4y=0.25(5)

0.1x+0.4y=1.25—----------------1

Step two

Also for the volume of the mixture, we are working with 5 gallons hence the expression

x+y=5-------------------------------2

The system of equation for the situation is

0.1x+0.4y=1.25------1

x+y=5-------------------2

From equation 2

x=5-y

Put x=5-y in the equation

0.1(5-y) +0.4y=1.25------1

0.5-0.1y+0.4y=1.25

0.3y=1.25-0.5

0.3y=0.75

Dividing both sides by 0. 3

y=0.75/0.3

y=2.5

x=5-y

x=5-2.5

x=2.5

The mixture should consist of

2.5 gallons of the first juice with

2.5 gallons of the second juice