ACT Preparation / Unit 15 ACT 1409 worked example, 60 to 90 seconds
The Score Needed for an Average
The idea
To find the value needed to reach a target average, work in three steps. First, multiply the target average by the total number of values, including the missing one, to get the required sum. Second, add the values already known. Third, subtract: the difference is the value needed. Check that it is possible, for example not above the highest possible score.
In practice
Worked example: a student's four test scores are 78, 85, 90 and 82. What score on the fifth test gives an average of 85? Required sum: 85 × 5 = 425. Known sum: 78 + 85 + 90 + 82 = 335. Needed: 425 − 335 = 90. For an average of 88, the need is 88 × 5 − 335 = 105, impossible on a 100-point test.
Where people slip
Multiply by the new count, five, not the old count, four: using four gives a required sum of 340 and a nonsense answer of 5.
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