Answer :
To find out how long it will take to check 80 parts when you can check 16 parts in 3 minutes, we can set up a proportion based on the rate of checking.
1. Determine the rate of checking parts:
You can check 16 parts in 3 minutes. Therefore, your rate is 16 parts per 3 minutes.
2. Set up a proportion to find the time for 80 parts:
We want to find out how many minutes it will take to check 80 parts.
[tex]\[
\frac{16 \text{ parts}}{3 \text{ minutes}} = \frac{80 \text{ parts}}{x \text{ minutes}}
\][/tex]
3. Solve the proportion:
To find [tex]\( x \)[/tex], cross-multiply and solve for [tex]\( x \)[/tex]:
[tex]\[
16 \times x = 80 \times 3
\][/tex]
[tex]\[
16x = 240
\][/tex]
Divide both sides by 16:
[tex]\[
x = \frac{240}{16}
\][/tex]
[tex]\[
x = 15
\][/tex]
4. Conclusion:
It will take 15 minutes to check 80 parts.
Thus, the best answer from the given choices is:
a. 15 minutes
1. Determine the rate of checking parts:
You can check 16 parts in 3 minutes. Therefore, your rate is 16 parts per 3 minutes.
2. Set up a proportion to find the time for 80 parts:
We want to find out how many minutes it will take to check 80 parts.
[tex]\[
\frac{16 \text{ parts}}{3 \text{ minutes}} = \frac{80 \text{ parts}}{x \text{ minutes}}
\][/tex]
3. Solve the proportion:
To find [tex]\( x \)[/tex], cross-multiply and solve for [tex]\( x \)[/tex]:
[tex]\[
16 \times x = 80 \times 3
\][/tex]
[tex]\[
16x = 240
\][/tex]
Divide both sides by 16:
[tex]\[
x = \frac{240}{16}
\][/tex]
[tex]\[
x = 15
\][/tex]
4. Conclusion:
It will take 15 minutes to check 80 parts.
Thus, the best answer from the given choices is:
a. 15 minutes
