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.
The answer is "They will walk 6 laps and run 18 laps." To find this, we can use a system of equations.
From the first row, we know that A + B = 3. From the second row, we know that C + D = 5.
From the third row, we know that A + C = 15 and B + D = 10.
Adding the equations A + B = 3 and B + D = 10, we get A + B + B + D = 13, which simplifies to A + 2B + D = 13.
Subtracting the equation C + D = 5 from A + C = 15, we get A + C - C - D = 10, which simplifies to A - D = 10.
Now we have the system of equations:
A + 2B + D = 13
A - D = 10
Solving this system of equations, we find that A = 4, B = 1, and D = -6. Since laps cannot be negative, we know that D must be 6 instead.
We can then substitute these values back into the equations to find C. From the equation A + C = 15, we know that A = 4, so C must be 11.
Therefore, the participants will walk 4 laps and run 6 laps.
If the total distance is 24 laps, the participants will walk 4/15 * 24 = 6.4 laps and run 6/5 * 24 = 28.8 laps.
Since we can't have fractional laps, the closest whole number to 6.4 is 6 and the closest whole number to 28.8 is 29.
So, the participants will walk 6 laps and run 29 laps.
To find out how many laps the participants will walk and run if the total distance is 24 laps, we need to solve the system of equations based on the given table:
A + C = 40 (equation 1)
3 + B + 15 = A (equation 2)
5 + 10 + D = C (equation 3)
From equation 1, we can solve for A:
A = 40 - C
Substituting this value of A into equation 2, we get:
3 + B + 15 = 40 - C
Simplifying, we have:
B + C = 22 (equation 4)
Substituting the value of D from equation 3 into equation 4, we have:
B + 10 + 5 = 22
Simplifying, we get:
B = 7
Substituting the value of B into equation 2, we have:
3 + 7 + 15 = A
Simplifying, we get:
A = 25
Now, substituting the values of A and C into equation 1, we have:
25 + C = 40
Simplifying, we get:
C = 15
So, the participants will walk 25 laps and run 15 laps.
However, none of the given options match this result. Therefore, none of the options provided is correct.