Apharmacist wants to mix a 16% saline solution with a 26% saline solution to get 15 l of a 20% saline solution. how much of each solution should she use?

the pharmacist wants to mix 2 solutions to make 15 L of a solution with 20% percentage

so if he mixes a volume of y of 16%, the quantity of solute added from the 16% solution is 16% x y = 0.16y

and he mixes a volume of z of 26%, the quantity of solute added from 26 % solution is 26% x z = 0.26z

the final solution has a solute quantity of 20 % x 15 L = 0.2 x 15 = 3

quantities of solute added from both solutions is equal to the quantity of the final solution

0.16y + 0.26z = 3 ---1)

the 2 volumes added equals 15 L

y + z = 15 ---2)

then we have a set of simultaneos equations

multiply 2nd equation by 0.16

0.16y + 0.16z = 2.4 --3)

subtract 3rd equation from the 1st equation

0.26 z - 0.16z = 0.6

0.10 z = 0.6

z = 0.6/0.10 = 6

since z = 6

then substitute z = 6 in 2nd equation

y + z = 15

y + 6 = 15

y = 9

the volume of 26% solution added is 6 L

volume of 16 % solution added is 9 L

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j