Question

A chemist wishes to make 3L of a 7% acid solution by mixing a 9% and a 4% acid solution. How many litres of each solution should the chemist use? My answer is 2.4L for the 4% solution and 600mL for the 9% solution. I used the allegation method. However when I tried to double check my answers, retracing it, the numbers became whacky. Anyone has an idea why?

Answer 1

that was wrong
i would solve
\[.09x+.04(3-x)=3\times .07\] for \(x\) but @FoolForMath is the master or allegation
frankly i had never heard of it before he mentioned it

Answer 2

this method is easy enough though, start with
\[9x+4(3-x)=21\] and you will be done in a trice

Answer 3

I think allegation is easier, lol. Yours looks complicated with all the symbols. Tic, tac, toe!

Answer 4

what? it is a simple linear equation, like from elementary algebra

Answer 5

but if you think allegation is easier, then be my guest

Answer 6

Elementary is primary school right?

Answer 7

can also solve
\[7x+3y=21\]
\[x+y=3\] but it is clearly the same

Answer 8

primary school if you go to a real school
US public school, might see it in 7th or 8th grade
inner city school you will see it when you take remedial classes at the local community college

Answer 9

that can't be right since total is 3

Answer 10

that's what I did! Than it turned downfall with the division, let me see if I can get a pic

Answer 11

your total is 7!

Answer 12

4.2+2.8=7L

Answer 13

A chemist wishes to make 3L of a 7% acid

Answer 14

No, no it's 7% acid solution, 3L of the solution

Answer 15

right so answer cannot be 4.2 liters of one and 2.8 liters of the other

Answer 16

i am sure it is superfast, but i don't know how to do it. i am sure @FoolForMath can adjust, but the answer is not that

Answer 17

I got an answer that makes sense 2400ml and 600 ml = 3L, but I can't get the same results when I double check it.

Answer 18

\[9x+4(3-x)=21\]
\[9x+12-3x=21\]
\[6x+12=21\]
\[6x=9\]
\[x=1.5\]

Answer 19

1.5 liters of 9% and the rest (1.5 also) liters of 4%

Answer 20

damn i messed up

Answer 21

Huh? I think I take the mess up Trophy here. Huh?

Answer 22

I multiplied with 7 in the last step, it should be 3.

Answer 23

\[9x+4(3-x)=21\]
\[9x+12-4x=21\]
\[5x=9\]
\[x=1.8\] there! helps to know the distributive law

Answer 24

so my answers wrong than?

Answer 25

Let me do this again,



9% ----> \(\frac 3 5 \times 3 =1.8 L\)

4% ----> \(\frac 2 5 \times 3 = 1.2 L\)