Question

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

A. 5/6B. 1/5C. 1/6D. 1/7E. 1/24

Answer 1

Option D.

Explanation:

It is given that a satellite is composed of 30 modular units. Each unit contains the same number of non-upgraded sensors.

Let x be the total number of upgraded sensors on the entire satellite.

The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite.

Non-upgraded sensors on one unit =
`(1)/(5)x`

Non-upgraded sensors on 30 unit =
`30* (1)/(5)x=6x`

Total number of sensors on the entire satellite is the sum of upgraded and non-upgraded sensors

`Total=x + 6x = 7x`

We need to find the fraction of the sensors on the satellite have been upgraded.

`Fraction=\frac{\text{Upgraded sensors}}{\text{Total sensors}}`

`Fraction=(x)/(7x)`

`Fraction=(1)/(7)`

Therefore, the correct option is D.