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?

Rationale

George sold 8 cars that month.

To find out how many cars George sold, we need to solve the equation given by his earnings function, m(x) = 7220 + 50x, for the month when his total earnings were $7,620. By substituting 7,620 for m(x) and solving for x, we discover that George sold 8 cars.

A (6) YOUR ANSWER

If George sold 6 cars, we can calculate his earnings as m(6) = 7220 + 50(6) = 7220 + 300 = 7520 dollars. This amount is less than the stated earnings of $7,620, indicating that selling 6 cars does not match his actual earnings that month.

B (7) YOUR ANSWER

For 7 cars, the calculation is m(7) = 7220 + 50(7) = 7220 + 350 = 7570 dollars. This figure still falls short of the $7,620 earnings, confirming that selling 7 cars would not produce the correct total for that month.

C (8) CORRECT

With 8 cars sold, we find m(8) = 7220 + 50(8) = 7220 + 400 = 7620 dollars. This matches the reported earnings perfectly, confirming that George sold 8 cars that month.

D (12) YOUR ANSWER

If George sold 12 cars, his earnings would be m(12) = 7220 + 50(12) = 7220 + 600 = 7820 dollars. This amount exceeds the actual earnings of $7,620, indicating that selling 12 cars is not a viable option for that month.

Conclusion

By solving the earnings function for the month when George earned $7,620, we determine that he sold 8 cars. The calculations for 6, 7, and 12 cars show earnings that do not correspond to the total reported, while the calculation for 8 cars perfectly aligns with his earnings for that month. This example illustrates the importance of accurately applying linear functions to solve real-world problems.

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?

George sold 8 cars that month.

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