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

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> 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      Log On


   

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) About Me  (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 x%2By=9. Solving for "y" gets us y=-x%2B9

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 0.06x%2B0.03y=0.04%28x%2By%29


0.06x%2B0.03y=0.04%28x%2By%29 Start with the second equation.


0.06x%2B0.03y=0.04x%2B0.04y Distribute


6x%2B3y=4x%2B4y Multiply EVERY term by 100 to make every number a whole number.


6x%2B3%28-x%2B9%29=4x%2B4%28-x%2B9%29 Plug in y=-x%2B9


6x-3x%2B27=4x-4x%2B36 Distribute.


3x%2B27=4x-4x%2B36 Combine like terms on the left side.


3x%2B27=0x%2B36 Combine like terms on the right side.


3x=0x%2B36-27 Subtract 27 from both sides.


3x-0x=36-27 Subtract 0x from both sides.


3x=36-27 Combine like terms on the left side.


3x=9 Combine like terms on the right side.


x=%289%29%2F%283%29 Divide both sides by 3 to isolate x.


x=3 Reduce.


y=-x%2B9 Go back to the isolated equation


y=-3%2B9 Plug in x=3


y=6 Combine like terms.


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Answer:


So the solutions are x=3 and y=6


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