Q:

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. What do the unknowns in this system represent and what are the two equations that that need to be solved? Finally, solve the system of equations.

Accepted Solution

A:
Answer:The amount of water in 3 liter spray is 1.95 liter and the amount of cleaner is 1.05 liter....Step-by-step explanation:Let x be the number of liters of waterLet y be the number of liters of cleanserThen the first equation we get is:x+y = twhere t is the total number of litersAnd we have given that 3-liter spray bottle  gives a second relationship.It means t=3 (second equation)These two equations will be solved simultaneously:Put the value t=3 in first equation:x+y= tx+y = 3We know that we have x = 0.65t and y =0.35t.Replace t with 3x=0.65(3)x= 1.95y=0.35(3)y=1.05Thus the amount of water in 3 liter spray is 1.95 liter and the amount of cleaner is 1.05 liter....