Problem:
If it takes 4 people 32 minutes to solve 16 problems, how many minutes will it take 8 people to solve 24 problems?
Solution:
Step 1: Write the given.
[tex]minutes(t)= 32\\problems(n)= 16\\people(p)= 4[/tex]
Step 2: Know what we were going to find.
[tex]minutes(t)= ?\\problems(n)= 24\\people(p)= 8[/tex]
Step 3: Write the formula.
[tex]m=\frac{nk}{p} \\m=minutes\\n=problems\\p=people\\k=constant[/tex]
Step 4: First, find the constant (k).
[tex]m=\frac{nk}{p} \\32=\frac{16k}{4} \\32=4k \\k=8[/tex]
Step 5: Then, find the minutes.
[tex]m=\frac{nk}{p} \\m=\frac{24(8)}{8} \\m=\frac{192}{8} \\m=24[/tex]
Answer:
The 8 people will take 24 minutes to solve 24 problems.
