Question

An office and apartment building is made up of modules. Each module is a rectangular prism. The building has 150 modules, and is 15 stories high. If all of the modules were divided evenly among the number of stories, how many modules would be on each floor? How many different rectangular prisms could be made from that number?

Answer 1

Part 1) 10 modules per floor

Part 2) Two different rectangular prism

Explanation:

Part 1)

Let

x ----> the number of modules

y ---> the number of stories

we have

`x=150\ modules\\y=15\ stories`

Divide the number of modules by the number of stories

so

`(x)/(y)=(150)/(15)=10\ (modules)/(floor)`

Part 2) How many different rectangular prisms could be made from that number?

The number is 10

Look at the factors of 10

They are 1,2 ,4,5 and 10

Pick any two of these factors and determine if there is a third value from this list so that the product of the three factors is 10

There are 2 combinations that will work :

1 0×1×1

2 ×5×1