New SAT Math Workbook

Example find the average of 12 17 and 61 solution 12

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Unformatted text preview: average is halfway between the two middle numbers. Example: Find the average of the first 40 positive even integers. Solution: Since these 40 addends are evenly spaced, the average will be half way between the 20th and 21st even integers. The 20th even integer is 40 (use your fingers to count if needed) and the 21st is 42, so the average of the first 40 positive even integers that range from 2 to 80 is 41. The above concept must be clearly understood as it would use up much too much time to add the 40 numbers and divide by 40. Using the method described, it is no harder to find the average of 100 evenly spaced terms than it is of 40 terms. In finding averages, be sure the numbers being added are all of the same form or in terms of the same units. To average fractions and decimals, they must all be written as fractions or all as decimals. Example: Solution: Rewrite each number as a decimal before adding. .875 .25 + .6 3)1.725 .575 Find the average of 87 %, 1 2 1 , and .6 4 www.petersons.com 106 Chapter 7 Exercise 1 Work out each problem. Circle the letter that appears before your answer. 1. Find the average of .49 , , and 80%. 4 (A) .72 (B) .75 (C) .78 (D) .075 (E) .073 Find the average of the first 5 positive integers that end in 3. (A) 3 (B) 13 (C) 18 (D) 23 (E) 28 The five men on a basketball team weigh 160, 185, 210, 200, and 195 pounds. Find the average weight of these players. (A) 190 (B) 192 (C) 195 (D) 198 (E) 180 3 4. Find the average of a, 2a, 3a, 4a, and 5a. (A) 3a5 (B) 3a (C) 2.8a (D) 2.8a5 (E) 3 Find the average of (A) (B) (C) (D) (E) 1 9 13 36 1 27 13 12 1 3 11 1 , , and . 23 4 2. 5. 3. www.petersons.com Averages 107 2. TO FIND A MISSING NUMBER WHEN AN AVERAGE IS GIVEN In solving this type of problem, it is easiest to use an algebraic equation that applies the definition of average. That is, average = Example: The average of four numbers is 26. If three of the numbers are 50, 12, and 28, find the fourth number. Solution: 50 + 12 + 28 + x = 26 4 50 + 12 + 28 + x = 104 90 + x = 104 x = 14 sum of terms number of terms An alternative method of solution is to realize that the number o...
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