A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars he checks, 4 have defects. If 10,500 cars will be checked this month, predict the total number of cars that will have defects.

Answer 1

To predict the total number of cars with defects in 10,500 cars, we first need to determine the proportion of cars with defects from the initial 280 cars checked.

The number of cars with defects is:

• Defective cars: 4
• Total cars checked: 280

The proportion of defective cars is calculated as: \[ \text{Proportion of defective cars} = \frac{\text{Number of defective cars}}{\text{Total cars checked}} = \frac{4}{280} \] Calculating this gives: \[ \frac{4}{280} = \frac{1}{70} \]

Now, we apply this proportion to the total number of cars that will be checked this month, which is 10,500 cars.

We can estimate the total number of defective cars by multiplying the total number of cars by the proportion of defective cars: \[ \text{Estimated number of defective cars} = 10,500 \times \frac{1}{70} \] Calculating this gives: \[ 10,500 \div 70 = 150 \]

Therefore, the predicted total number of cars that will have defects is: \[ \boxed{150} \]