Gabe amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. how many liters of each does he need to make the needed 30 liters of 60% acid solution?

x = liters of 40% solution

y = liters of 70% solution

Gabe needs 30 liters, so

x + y = 30

Each liter of 40% solution contributes 0.4x liter of acid; each liter of 70% solution contributes 0.7y liter of acid. Gabe needs a solution with concentration 60%, which from 30 liters amounts to a net volume of 0.6*30 = 18 liters of acid. So

0.4x + 0.7y = 18

Solve the system however you like. By substitution, we have

y = 30 - x

0.4x + 0.7(30 - x) = 18

0.4x + 21 - 0.7x = 18

3 = 0.3x

==> x = 10 ==> y = 20

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.