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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?

Respuesta :

y = 12% = 0.12

y = 100(0.05) + x(0.2) / 100 + x
0.12 = 5 + 0.2x / 100 + x
0.12( 100 + x ) = 5 + 0.2x
12 + 0.12x = 5 + 0.2x
7 = 0.08x
x = 87.5

hope this help

Answer:

87.5 ml is needed

Step-by-step explanation:

Given : You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function [tex]y =100(0.05)+\frac{(0.2)x}{100+x}[/tex] gives the concentration y of blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye.

To find : How much of the 20% dye must you add to get a dye that is 12% concentrated?

Solution :

Let x be the concentration.

According to question,

y = 12% = 0.12  

We have given,

[tex]y =\frac{100(0.05)+(0.2)x}{100+x}[/tex]

Put y=0.12,

[tex]0.12=\frac{100(0.05)+(0.2)x}{100+x}[/tex]

[tex]0.12\times (100+x)=5+(0.2)x[/tex]

[tex]12+0.12x=5+(0.2)x[/tex]

[tex]12-5=(0.2)x-0.12x[/tex]

[tex]7=0.08x[/tex]

[tex]x=\frac{7}{0.08}[/tex]

[tex]x=87.5[/tex]

Therefore, 87.5 ml is needed.

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