SOLUTION: When solving systems of we have at least two unknowns. A common example of a system of equations is a mixture problem. If I know that the solution I use to clean my car windows is

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Question 1141820: When solving systems of we have at least two unknowns. A common example of a system of equations is a mixture problem. If I know that the solution I use to clean my car windows is 65% water and 35% cleaner, I have one relationship. If I also know that I only have a 3-liter spray bottle that gives me a second relationship.
1. What do the unknowns in this system represent and what are the two equations that that need to be solved?
2. Finally, solve the system of equations.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

            If you want to learn on how to setup and how to solve the mixture word problems,

            there is a NICE source for it.


This source is THESE LESSONS
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them and become an expert in solution the mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
w = number of liters of water.
c = number of liters of cleaner.

first equation is w + c = t

this tells you that the number of liters of water plus the number of liters of cleaner equals a total of t liters.

you are then given that t = 3.

these are 2 equations that need to be solved simultaneously.

replace t in the first equation with t = 3 from the second equation and you get:

w + c = 3

you are then given that w = .65 * t and c = .35 * t

replace t with 3 and the equations becomes w = .65 * 3 and c = .35 * 3.

solve for w and c to get w = 1.95 and c = 1.05.

that's your solution.

the amount of water in the 3 liter spray bottle is 1.95 liters.
the amount of cleaner in the 3 liter spray bottle is 1.05 liters.