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.

Question

Mathematics

Rory Bowman

4 March, 00:05

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.

+1

Answers (1)

Know the Answer?

Elian Trevino · Answer 1

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 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 ...