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?

Answer 1

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 2

87.5 ml is needed

Explanation:

Given : 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)+((0.2)x)/(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.

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,

`y =(100(0.05)+(0.2)x)/(100+x)`

Put y=0.12,

`0.12=(100(0.05)+(0.2)x)/(100+x)`

`0.12* (100+x)=5+(0.2)x`

`12+0.12x=5+(0.2)x`

`12-5=(0.2)x-0.12x`

`7=0.08x`

`x=(7)/(0.08)`

`x=87.5`

Therefore, 87.5 ml is needed.