Question

Blake made an 87 on the first semester of Algebra I. What score can he make in the second semester if he wants his average to be more than a 90 for both semsters?

What is the inequality and answer?

Answer 1

x>95

Explanation:

94 s equal to 90

Answer 2

• inequality: (87 +s)/2 > 90
• answer: Blake can make any score more than 93

Explanation:

Assuming the semester scores have equal weights, for a second-semester score of s, Blake wants ...

(87 +s)/2 > 90 . . . . average for both semesters

87 +s > 180 . . . multiply by 2

s > 93 . . . . . . subtract 87

Blake's score must be more than 93 for his average to be more than 90.

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Alternate solution

Blake's current score is 90 - 87 = 3 points below the average he wants. To get the average he wants, his second score must be more than 3 points above the average he wants: 90 + 3 = 93. He must make more than 93.

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In any set of data, the total of signed deviations from average will be zero.

Here we have 2 data values, one of which deviates -3 from the average. That means the other must deviate +3 from the average, so the total deviation is -3+3 = 0.