8. George sells previously owned cars. Each month his earnings, in dollars, are given by the function m(x)=7220+50x, where x is the number of cars George sells that month. One month his total monthly earnings were $7,620. How many cars did George sell that month?
Answer: C
George sold 8 cars that month.
To find out how many cars George sold, we set his earnings function equal to his total earnings of $7,620 and solve for x. This leads us to determine that George sold 8 cars.
A) 6
If George sold 6 cars, we can calculate his earnings using the function m(x)=7220+50x. Substituting x with 6 gives m(6)=7220+50(6)=7220+300=7520. This amount is less than $7,620, making this option incorrect.
B) 7
Calculating for 7 cars, we use the same function: m(7)=7220+50(7)=7220+350=7570. This total also does not match $7,620, so this option is incorrect.
C) 8
For 8 cars, we calculate m(8)=7220+50(8)=7220+400=7620. This matches exactly with George's earnings of $7,620, confirming that he sold 8 cars that month, making this option correct.
D) 12
If George sold 12 cars, we find his earnings by calculating m(12)=7220+50(12)=7220+600=7820. This total exceeds $7,620, indicating that this option is incorrect.
Conclusion
The correct answer is 8 cars, as it is the only option that, when plugged into the earnings function, results in the total earnings of $7,620. All other options either fall short or exceed the specified earnings, confirming that they cannot be correct.