Ask your own question, for FREE!
Mathematics 20 Online
OpenStudy (anonymous):

I'm stuck! Suppose a lab needs to make 900 liters of a 39% acid solution, but the only solutions available to the lab are 15% acid and 70% acid. What system of equations can be used to find the number of liters of each solution that should be mixed to make the 39% solution? Let c represent the number of liters of 15% acid solution and let d represent the number of liters of 70% acid solution.

OpenStudy (imstuck):

I can give you the equation in terms of one variable going from a table, but am having difficulty using two variables, for some odd reason.

OpenStudy (imstuck):

oh wait...duh...this is it!

OpenStudy (imstuck):

c + d = 900 (relating the amounts of liquid) .15c + .70d = .39(900)

OpenStudy (imstuck):

Say that c = 900-d, fill in that amount for c in the second equation to get this:

OpenStudy (imstuck):

.15(900-d)+.7d=351

OpenStudy (imstuck):

Doing that math gives you

OpenStudy (imstuck):

135-.15d+.7d=351 and .55d = 216 d = 392.7

OpenStudy (imstuck):

That is how much of the 70% acid solution that needs to be mixed in with the 15% acid of which there is 900-392.7=507.3

OpenStudy (anonymous):

these are the options but I say that it is B

OpenStudy (imstuck):

507.3 liters of 15% acid + 392.7 liters of 70% acid = 900 liters of 39% acid

OpenStudy (imstuck):

No its not B; it's the last choice; that one is exactly what I did to solve this. It's the very last choice. Check it against my work and then do the math yourself to see that it is correct.

OpenStudy (anonymous):

okay Im going to try to do it and see but thank you so much you're a big help!

OpenStudy (jdoe0001):

\(\large { \begin{array}{cccccllll} &liters\ needed&acidity&total\ liters \\\hline\\ 15\%&c&0.15&0.15c\\ 70\%&d&0.70&0.70d\\ mixture&c+d=900&0.39&0.39(900)=351 \end{array}\\ \quad \\ c+d=900\implies c=900-d\qquad thus \\ \quad \\ \begin{array}{cccccllll} &liters\ needed&acidity&total\ liters \\\hline\\ 15\%&900-d&0.15&0.15(900-d)\\ 70\%&d&0.70&0.70d\\ mixture&(900-d)+d=900&0.39&0.39(900)=351 \end{array} \\ \quad \\ \implies {\color{brown}{ 0.15(900-d)+0.70d=351}} }\)

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
euphoriiic: I drew more people !! ud83eudd17.
11 minutes ago 40 Replies 3 Medals
euphoriiic: I drew markk ud83eudd17.
1 hour ago 34 Replies 2 Medals
LOLIAteYourMom: u2212243 = u22129(10 + x)
4 hours ago 0 Replies 0 Medals
Bubblezz: Art for @jeromeccv
4 hours ago 13 Replies 3 Medals
Bubblezz: Art for @jeromecv
8 hours ago 0 Replies 0 Medals
MakaylaChuck23: no
3 hours ago 9 Replies 0 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!