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?

You should mix

2.5 gallons of the first juice with

2.5 gallons of the second juice

Step-by-step 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=52

The system of equation for the situation is

0.1x+0.4y=1.251

x+y=52

From equation 2

x=5-y

Put x=5-y in the equation

0.1(5-y) +0.4y=1.251

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

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

its line 2 i just added the rest or else it wouldn't let me answer