Question

A pharmacist has 40% and 60% iodine solutions on hand. How many liters of each item solution will be required to produce 8 L of a 50% iodine mixture

Answer 1

Answer:

The quantity of 40 % solution is 4 liters    and

The quantity of 60 % solution is 4 liters .

Step-by-step explanation:

Given as

A pharmacist has 40% and 60% iodine solutions on hand.

Let the quantity of 40 % iodine solutions = x liter

And The quantity of 60 % iodine solutions = y liter

The total quantity of iodine mixture = 8 liter

I.e  The quantity of 40 % iodine solutions +  the quantity of 60 % iodine solutions = 8 Liter

or  x + y = 8

The The percentage of mixture solution = 50 %

∴ 40 % of x + 60 % of y = 50 % of 8

I.e 40 x + 60 y = 400         ..........A

And x + y = 8

Or, 40× ( x + y ) = 40× 8

or, 40 x + 40 y = 320       ...........B

Now , solving equations A and B

I.e (  40 x + 60 y ) - (  40 x + 40 y ) = 400 - 320

Or, (  40 x - 40 x ) + (  60 y - 40 y ) = 80

Or, 0 + 20 y = 80

∴  y = $\frac{80}{20}$

I.e  y = 4 liters

So, The quantity of 60 % iodine solution = y = 4 liters

Put The value of y in Eq A

So ,  40 x + 60 × 4 = 400

Or, 40 x = 400 - 240

or, 40 x = 160

∴  x = $\frac{160}{40}$

I.e  x = 4 liter

So, The quantity of 40 % iodine solution = x = 4 liters

Hence The quantity of 40 % solution is 4 liters and the quantity of 60 % solution is 4 liters . Answer