It's a word problem, read the description - xx thank you in advance.

Question

You are making 6 quarts of fruit punch for a party. You have bottles of 100% fruit juice and 20% fruit juice. How many quarts of each kind of juice should you mix to make 6 quarts of 80% fruit juice?

 

 

It's system of equations, I need two equations. Variables. X - 100% fruit juice and Y = 20% fruit juice. 

If you do this right, thank you so much. 

 

Answer 1

So we need to find quarts for each kind of juice. You're right we need 2 equations.

 

This equation is to calculate the amount of quarts.

 

X+Y=6 

 

X is the number of quarts of 100%  fruit juice.

Y is the number of quarts of 20% fruit juice.

 

We need a total of 6 so that is where this equation comes from.

 

The second equation is to calculate how much quarts of fruit juice to get 80% fruit juice.

 

X(100%)+Y(20%)=80%  However, 80% is going to be the average so we will have divide the equation by 6.

 

 

(X(100%)+Y(20%))/6=80%

 

To make it easier we will multiply 6 to both sides, the 6  on the left side cancels out and we end up with:

 

X(100%)+Y(20%)=480%

 

Now we go back to the original equation:

X+Y=6

 

We set it equal to X or Y (I'm choosing X)

X=6-Y

 

Now lets take this X and put it into this equation: X(100%)+Y(20%)=480%

 

We end up with:  (6-y)(100%)+Y(20%)=480%

Now Solve for Y: 600-100Y+20Y=480

600-80Y=480

-80Y=-120

Y=1.5 So we need 1.5 quarts of Y( 20% fruit juice). If we use X+Y=6

 

We need 4.5 quarts of X(100% fruit juice)

 

So we end up with 1.5 quarts of 20% fruit juice and  4.5 quarts of 100% fruit juice

 

You can check.

 

X(100%)+Y(20%)=480% ==>   (4.5)(100%)+(1.5)(20%)=480% ==> 480=480

 

I think that's it. Good Luck!