Im on the verge of tears and i️ just want to be done with this! a pharmacist wishes to mix a solution that is 8% minoxidil. she has on hand 100 ml of a 7% solution and wished to add some 10% solution to obtain the desired 8% solution. how much 10% solution should she add?

100 (.07) + x (.10) = (100+x) (.08)

Amount * percent + amount* percent = (total amount) * desired percent

distribute

7 + .1 x = 8+.08x

subtract .08x from each side

7 +.02x = 8

subtract 7 from each side

.02x =1

divide by .02

x = 1/.02

x = 50

add 50 ml of the 10% solution

50mL of 8% solution

Step-by-step explanation:

Givens

Let the number of mL of 10% solution needed = x

Let the number of mL of 7% solution to be used = 100

She needs an 8% solution.

10%*x + 100*7% = (100 + x)*8%

(10/100)*x + 100*7/100 = 100*8/100 + x*8/100   Multiply through by 100

10x + 700 = 800 + 8x                     Subtract 700 from both sides

10x + 700 - 700 = 800 - 700 + 8x

10x  = 100 + 8x                                 Subtract 8x from both sides.

10x - 8x = 100                                    Combine like terms on the left

2x = 100                                            Divide by 2

x = 100/2                                           Do the division

x = 50

You need to add 50 Ml of the 10% solution.

Check

Left Hand Side

100 mL of 7% = 7 mL of active ingredient.

50 mL of 10% = 5 mL of active ingredient

Total                   12 mL of active ingredient

Right Hand Side

150 mL of 8% = 12 mL of active ingredient

And it checks.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225