The school football coach wants to know how many hours he trained Lyle and Trent this season. This season, each training session was 2 hours. There was also one mandatory weekend workout that counted for 6 hours of training.
Lyle and Trent both attended the weekend workout, but attended different numbers of training sessions.
This season, Lyle had at least 42 hours of training.
Trent attended at least twice as many training sessions as Lyle.
Graph the possible number of Trent's hours of training on the number line provided.
Let's represent the number of training sessions attended by Lyle as L and the number of training sessions attended by Trent as T.
We know that each training session is 2 hours, so Lyle's hours of training can be represented as 2L.
We also know that Trent attended at least twice as many training sessions as Lyle, so T is greater than or equal to 2L.
The weekend workout counted for 6 hours, so Trent's hours of training can be represented as 2T + 6.
Since Lyle had at least 42 hours of training, we have:
2L ≥ 42
We can solve this inequality for L:
L ≥ 21
Substituting this into our equation for Trent's hours of training:
2T + 6 ≥ 2(21) + 6
2T + 6 ≥ 42 + 6
2T + 6 ≥ 48
Simplifying:
2T ≥ 42
Dividing both sides by 2:
T ≥ 21
From this, we can see that the possible number of Trent's hours of training lies between 21 and infinity on the number line.
21 isn't available on the number line. its only numbers 50 through 90.
I apologize for the confusion. Let's update the number line accordingly.
Since Lyle had at least 42 hours of training, we have:
2L ≥ 42
We can solve this inequality for L:
L ≥ 21
Since Trent attended at least twice as many training sessions as Lyle, we have:
T ≥ 2L
Substituting L ≥ 21 into this inequality:
T ≥ 2(21)
T ≥ 42
So the possible numbers of Trent's hours of training are represented by all numbers greater than or equal to 42 on the number line between 50 and 90.
42 isnt on the number line.
Apologies for the confusion again. Let's revise the number line.
Since Lyle had at least 42 hours of training, we have:
2L ≥ 42
Simplifying, we get:
L ≥ 21
Since Trent attended at least twice as many training sessions as Lyle:
T ≥ 2L
Substituting L ≥ 21 into this inequality:
T ≥ 2(21)
T ≥ 42
On the number line provided, the possible numbers of Trent's hours of training would be represented between 50 and 90. Since 42 is not on the number line, we can see that Trent's hours of training can range from 50 to 90 or any value greater than or equal to 50.