Question

The product of three positive numbers is 2560. One of those numbers, z, is 60 percent greater than the product of the other two numbers. What is the value of z?

Answer 1

64

Explanation:

Let x,y and z represent the product of three positive numbers so

`xyz = 2560`

We also know z is 60% greater than product of the other two numbers.

Let this be

`z = (1.6)xy`

We must find the value of z.

Subsitue (1.6)xy for z.

`(xy)(xy)(1.6) = 2560`

`1.6 {x}^(2) {y}^(2) = 2560`

`{x}^(2) {y}^(2) = 1600`

`xy = 40`

Now subsitue this in to any our orginal equation.solve for

`1.6(40) = z`

`64 = z`

or we can

`xyz = 2560`

`40(z) = 2560`

`z = 64`

So our z value is 64