The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk and run if the total distance is 24 laps?
They will walk 7 laps and run 17 laps.
They will walk 15 laps and run 9 laps.
They will walk 9 laps and run 15 laps.
They will walk 6 laps and run 18 laps.
To find the number of laps the participants will walk and run if the total distance is 24 laps, we need to solve the system of equations represented by the table.
From the table we have the following equations:
A + C = 40 (total laps equation)
3 + B + 15 = A (walk equation)
5 + 10 + D = C (run equation)
We can substitute the value of A from the walk equation into the total laps equation to get:
3 + B + 15 + C = 40
Simplifying this equation, we get:
B + C = 22
Now, we substitute the value of C from the run equation into the above equation to get:
B + (5 + 10 + D) = 22
Simplifying this equation, we get:
B + D = 7
So now we have the following two equations:
B + C = 22
B + D = 7
From these equations, we can solve for B and D by substitution or elimination.
Subtracting the second equation from the first equation, we get:
(B + C) - (B + D) = 22 - 7
C - D = 15
From this equation, we can see that if the participants walk 15 laps, they will run 0 laps since D would be 0. However, this does not satisfy the total distance of 24 laps. Therefore, none of the given options is correct.
Thus, the correct answer is: None of the above
To find out how many laps the participants will walk and run if the total distance is 24 laps, we need to solve the given table.
From the table, we know that:
Walk (laps) + Run (laps) = Total (laps)
We also know that:
3 + 5 = 8
15 + 10 = 25
A + C = 40
To find the values of A and C, we can subtract 8 and 25 from 40:
40 - 8 = 32
40 - 25 = 15
So A = 32 and C = 15.
Now, we need to find out the laps the participants will walk and run if the total distance is 24 laps.
Let's set up an equation using the given information:
Walk (laps) + Run (laps) = Total (laps)
A + B = 24
We know that A = 32, so let's substitute that into the equation:
32 + B = 24
Now, let's solve for B:
B = 24 - 32
B = -8
Since B is -8, this means that we cannot have negative laps. Therefore, none of the answer choices provided are correct.
The correct answer is: None of the options provided.