Martin uses 8 5/8 of a gallon of paint to cover 4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon?

32/345 wall per gallon

Step-by-step explanation:

Rate is defined as ratio between two quantities with different units.

Gallons of paint used by Martin = 8 5/8 gallons = 69/8 gallons

Portion of wall Martin wishes to pint = 4/5 wall

Rate at which Martin paints the wall:

= Portion of wall covered / paint used

=

4/5 / 69/8 = 32/345 wall per gallon

Martin paints 0.093 walls per gallon of paint

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of paint used by Martin = 8 5/8 of a gallon

Ratio of wall painted by Martin with 8 5/8 of a gallon = 4/5

2. What is the unit rate at which Martin paints in walls per gallon?

Let's convert the mixed fractions to decimals this way:

8 5/8 = 8 + 0.625 = 8.625

4/5 = 0.8

Now, let's use the Direct Rule of Three, this way:

Gallons                      Walls

8.625                          0.8

x                                   1

Solving for x :

0.8x = 8.625 * 1

x = 8.625/0.8

x = 10.78125

x = 10.8 (rounding to next tenth) gallons

For painting a wall, we will use 10.8 gallons of paint. Now, we can calculate the unit rate at which Martin paints in walls per gallon, this way:

Gallons                      Walls

10.8                               1

 1                                  x

Solving for x :

10.8x = 1

x = 1/10.8

x = 0.09259

x = 0.093 (rounding to the next hundredth) walls per gallon of paint