You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y =100(0.05)+x(0.2)/100+x gives the concentration y of blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated?

Question

You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y =100(0.05)+x(0.2)/100+x  gives the concentration y of blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated?

anonymous · Answer

That is a confusing problem to read, but when you get through all the words, it is really just saying that y = 12% or 0.12, and asking you to solve that function for x.

anonymous · Answer

the answers is
62.5 mL
75 mL
87.5 mL
112.5 mL

anonymous · Answer

$$y = \frac{ (100)(0.05) + x(0.2) }{ 100+x } = \frac{ 5 + 0.2x }{ 100+x }$$
$$0.12 =\frac{ 5+0.2x }{ 100+x }$$
$$0.12(100+x) = 5 + 0.2x$$
$$12+0.12x= 5 + 0.2x$$
$$7=0.08x$$
x = 87.5

anonymous · Answer

That's how you work it.  Hope that was helpful... try to learn how to set up and solve these.

anonymous · Answer

thank you