Question

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.

Answer 1

The amount of water in 3 liter spray is 1.95 liter and the amount of cleaner is 1.05 liter....

Explanation:

Let x be the number of liters of water

Let y be the number of liters of cleanser

Then the first equation we get is:

x+y = t

where t is the total number of liters

And 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= t

x+y = 3

We know that we have x = 0.65t and y =0.35t.

Replace t with 3

x=0.65(3)

x= 1.95

y=0.35(3)

y=1.05

Thus the amount of water in 3 liter spray is 1.95 liter and the amount of cleaner is 1.05 liter....