A painter used 1 1/2 gallons of paint to paint 3/4 of a room. At this same rate, how many gallons will it take to paint the whole room? Please show your work with descriptions, this topic of math is really confusing for me.

Convert to decimals:

1.5 and 0.75

Then, set up a proportion

1.5/0.75=x/1

proportion x/y=x/y

since the 3/4 and 1 are the same topic ( the room) we put them together.

Solve: 1.5/0.75=x

x=2

So 2 gallons

Hope this helps plz hit the crown :D

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!