SOLUTION: Mom made two baches of iced tea. the first contained 6% sugar and was too sweet the second contained 3% sugar and was too sour how many cups should she take from each batch to make

Question 202001: Mom made two baches of iced tea. the first contained 6% sugar and was too sweet the second contained 3% sugar and was too sour how many cups should she take from each batch to make 9 cups of iced tea containing 4% sugar.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

x = # of cups that contains 6% sugar
y = # of cups that contains 3% sugar

Since we want 9 cups total, this means . Solving for "y" gets us

Also, since we want to mix "x" cups of 6% sugar with "y" cups of 3% sugar to get 9 cups with 4% sugar, this means that

Start with the second equation.

Distribute

Multiply EVERY term by 100 to make every number a whole number.

Plug in

Distribute.

Combine like terms on the left side.

Combine like terms on the right side.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

Go back to the isolated equation

Plug in

Combine like terms.

===================================================================

Answer:

So the solutions are and

This means that 3 cups of tea with 6% sugar and 6 cups of tea with 3% sugar are needed.

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