Question 202001
Let


x = # of cups that contains 6% sugar

y = # of cups that contains 3% sugar



Since we want 9 cups total, this means {{{x+y=9}}}. Solving for "y" gets us {{{y=-x+9}}}


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+0.03y=0.04(x+y)}}}



{{{0.06x+0.03y=0.04(x+y)}}} Start with the second equation.



{{{0.06x+0.03y=0.04x+0.04y}}} Distribute



{{{6x+3y=4x+4y}}} Multiply EVERY term by 100 to make every number a whole number.



{{{6x+3(-x+9)=4x+4(-x+9)}}} Plug in {{{y=-x+9}}}



{{{6x-3x+27=4x-4x+36}}} Distribute.



{{{3x+27=4x-4x+36}}} Combine like terms on the left side.



{{{3x+27=0x+36}}} Combine like terms on the right side.



{{{3x=0x+36-27}}} 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=(9)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



{{{y=-x+9}}} Go back to the isolated equation



{{{y=-3+9}}} 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.