Lesson Solved problems on average scores, weight, height and temperature
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<H2>Solved problems on average scores, weight, height and temperature</H2> <H3>Problem 1</H3>The mean of seven numbers is 48. Six of them are 22, 36, 15, 24, 73, 84. Find the seventh. <B>Solution</B> <pre> You are given that the sum of the seven numbers divided by 7 is equal to 48. It means that the sum of the seven numbers is equal to 48*7 = 336. The six numbers are given. Then the seventh number = {{{48*7 - (22 + 36 + 15 + 24 + 73 + 84)}}} = 82. <U>Answer</U>. The seventh number is 82. </pre> <H3>Problem 2</H3>An average score on the mid exam of 25 students was 78.8 out of 100. After the exam however a student whose score was 41 out of 100 dropped the course. What is the average score of among remaining 24 students? <B>Solution</B> <pre> We are given that the sum of scores of 25 students, divided by 25, is equal to 78.8. It means that the sum of scores of 25 students is 78*25 = 1970. When one student dropped, the sum of scores of remaining 24 students is 1970 - 41 = 1929. Then the average score of the remaining 24 students is {{{1929/24}}} = 80.375. </pre> <H3>Problem 3</H3>Average weight of all students in a class is 43 kg. Four new students whose weights are 24 kg, 36.5kg, 39.5kg and 42kg join the class. Now, their average weight reduces by 500 gram. Find the number of students at the beginning. <B>Solution</B> <pre> Let n be the number of students in the class at the beginning. Then the condition says that the total weight of n students W, divided by n, is 43 kg: {{{W/n}}} = 43, or, which is the same, W = 43n. (1) To account for the weight of the four additional students, we must add the given numbers to W and then to divide it by (n+4) to get the new average. It gives an equation {{{(43n+24+36+39.5+42)/(n+4)=(43-0.5)}}}, or, which is the same, {{{(43n + 141.5)/(n+4)}}} = 42.5. To solve it, multiply both sides by (n+4) and then simplify: 43n + 141.5 = 42.5*(n+4), 43n + 141.5 = 42.5n + 170, 43n - 42.5n = 170 - 141.5 ====> 0.5n = 28.5 ====> n = {{{28.5/0.5}}} = 57. <U>Answer</U>. 57 students were there in the class at the beginning. </pre> <H3>Problem 4</H3>The average temperature from Monday to Thursday is 48 degrees and from Tuesday to Friday is 52 degrees. If the temperature on Monday is 42 degrees, what was it on Friday ? <B>Solution</B> <pre> Let M be the temperature on Monday, T -------- '' --------- Tuesday W -------- '' --------- Wednesday H -------- '' --------- Thursday F -------- '' --------- Friday You are given {{{(M + T + W + H)/4}}} = 48, which implies M + T + W + H = 4*48 = 192. (1) You also are given {{{(T + W + H + F)/4}}} = 52, which implies T + W + H + F = 4*52 = 208. (2) Subtract equation (1) from equation (2). You will get F - M = 208 - 192, or, which is the same, F - M = 16. (3) Now substitute M = 42 into equation (3). You will get F - 42 = 16, which implies F = 16 + 42 = 58. <U>Answer</U>. The Friday temperature is 58 degrees Fahrenheit. </pre> My other lessons on <B>Average, Mean and Median</B> in this site are - <A HREF=https://www.algebra.com/algebra/homework/Average/Geometric-Mean.lesson>WHAT IS Geometric mean</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Difference-between-Amean-and-Gmean.lesson>Difference between Arithmetic mean and Geometric mean</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/What-is-Median.lesson>WHAT IS Median</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Solved-problems-on-average-scores.lesson>Solved problems on average scores</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Solved-problems-on-average-age.lesson>Solved problems on average age</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Miscellaneous-problems-on-average-values.lesson>Miscellaneous problems on average values</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Math-circle-level-problem-on-average.lesson>Math circle level problem on average</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Entertainment-problems-on-average.lesson>Entertainment problems on average</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/The-mean-and-the-total-value-problem-for-the-International-Fools-day-of-April-1.lesson>The mean and the total value problem for the International Fools' day of April, 1</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/OVERVIEW-of-lessons-on-Average-Mean-and-Median.lesson>OVERVIEW of lessons on Average</A>
