Marie has scores of 65,72,80,74, and 85 on five math tests. The final will count as two tests in determining each students overall average. What score must Marie get on the final if she wants her overall average to Ben 80?
80*7=(65+72+80+74 +85+2*F)
solve for F
To determine the score Marie must get on the final exam, we first need to calculate her current overall average.
Step 1: Add up Marie's scores on the five math tests:
65 + 72 + 80 + 74 + 85 = 376
Step 2: Since the final exam counts as two tests, we need to add two more scores before calculating the overall average. Let's denote her final exam score as x (out of 100).
Step 3: Calculate her overall score by adding her current score to the final exam score:
376 + x + x = 376 + 2x
Step 4: To find her overall average, we divide the total score by the number of tests:
Overall average = (376 + 2x) / 7
Step 5: Set up the equation to solve for x (the final exam score):
(376 + 2x) / 7 = 80
Step 6: Multiply both sides of the equation by 7 to get rid of the denominator:
376 + 2x = 560
Step 7: Subtract 376 from both sides of the equation:
2x = 560 - 376
2x = 184
Step 8: Divide both sides of the equation by 2 to solve for x:
x = 92
Therefore, Marie must get a score of 92 on the final exam to achieve an overall average of 80.