Question

Artificial turf in on athletic fields was first introduced in the 1960s. Its safety has been controversial since then. One issue that has been investigated is whether injuries of football players tend to be more serious on artificial turf than grass. A study followed 24 NCAA division 1A college football teams over three seasons

In total there were 1050 injuries that occurred on field turf. Of the field turf injuries, 83.3333% were minor and 10.857% were substantial.

77.972% of grass injuries were minor.

4.26% of injuries occurred on grass were severe.

(There is a total of minor injuries on grass and on field turf is equal to 1813.

How many injuries were severe and occurred on field turf? Write your answer as an integer.

How many injuries were severe? Write your answer as an integer.

Answer 1

1. Out of 1050 injuries that occurred on field turf:

`(1050)(0.8333) = 875` were minor and
`(1050)(0.10857) = 114` were substantial. This leaves 1050 - 875 - 114 = 61 severe injuries.

2. If there were 1813 total minor injuries, and 875 were on field turf, then 1813 - 875 = 938 were on grass. This is 77.972% of all grass injuries, so
`0.77972x = 938` gives
`x = 1203` total grass injuries.

Since 4.26% of grass injuries were severe, this is (1203)(0.0426) = 51 severe grass injuries. Adding this to the 61 severe turf injuries gives a total of 112 severe injuries.