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<H2>Miscellaneous problems on average values</H2> <H3>Problem 1</H3>Out of 13 cows one worth rs 26000 was removed and a horse was included. If the average price of animals increased by rs 15000, find the price of the horse. <B>Solution</B> <pre> Equation 1: 12 cows + 13-th cow cost together 13*X, where X is the average cost of 13 cows (now unknown). Equation 2: 12 cows + the horse cost together 13*Y, where Y is the average cost of 13 animals (now unknown). Subtract equation (1) from equation (2). You will get the horse price - the 13-th cow price = 13*(Y - X). In the last equation, you know that Y - X = 15000 (given !) and the 13-th cow price = 26000. Therefore, the horse price = 26000 + 13*15000 = 221000. <U>ANSWER</U> </pre> <H3>Problem 2</H3>Average monthly production of a certain factory for the first 9 months is 2584 units and for remaining three months it is 2416 units. Calculate average monthly production for the year. <B>Solution</B> <pre> Average for the year = Average for 12 months = {{{Total_for_12_months/12}}} = {{{(9*2584 + 3*2416)/12}}} = 2542 units. <U>ANSWER</U> </pre> <H3>Problem 3</H3>Average of 9 numbers is 301; average of first five numbers is 163, and average of last 5 numbers is 430. Find the value of the fifth number. <B>Solution</B> <pre> Let the 9 numbers are {{{a[1]}}}, {{{a[2]}}}, {{{a[3]}}}, {{{a[4]}}}, {{{a[5]}}}, {{{a[6]}}}, {{{a[7]}}}, {{{a[8]}}} and {{{a[9]}}}. Then from the condition P = {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} = 5*163 and Q = {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}} + {{{a[9]}}} = 5*430, while R = {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}} + {{{a[9]}}} = 9*301. Next, it is clear that P + Q - R = {{{a[5]}}} = 5*163 + 5*430 - 9*301, and the last expression in the right side is equal to 256. <U>Answer</U>. At given conditions, {{{a[5]}}} = 256. </pre> <H3>Problem 4</H3>In a class of 40 the average score was 70.25. The average scores for boys and girls were 68 and 73 respectively. How many boys were in the class ? <B>Solution</B>. <pre> Let x be the number of boys; then the number of girls is (40-x). Total scores of boys is 68x; total scores of girls is 73*(40-x). Total scores of the class is 40*70.25 = 2810. The equation of total scores is 68x + 73*(40-x) = 2810. From the equation x = {{{(2810-73*40)/(68-73)}}} = 22. <U>ANSWER</U>. There are 22 boys in the class. </pre> <H3>Problem 5</H3>The Syracuse Panthers baseball team won 54 games and lost 16 games. If they want to get an 80% winning average, how many more games do they have to win without any losses? <B>Solution</B> <pre> Let x = "how many more games". The equation to solve is {{{(54+x)/(54+16+x)}}} = 0.8. Simplify and find x 54+x = 0.8*(70+x) 54 + x = 56 + 0.8x x - 0.8x = 56 - 54 0.2x = 2 x = 2/0.2 = 10. <U>ANSWER</U>. 10 games to win without any loss. </pre> <H3>Problem 6</H3>A B-747 airplane is fully refueled before takeoff. The 747 uses approximately 60 gallons of fuel per minute while flying at the speed of 600 mph and approximately 50 gallons per minute while flying at the speed of 500 mph. The plane flies for 3 hours at the rate of 600 mph and then slows down for the last 2 hours to 500 mph. On this entire flight what was the average number of gallons per mile used by the airplane? <B>Solution</B> <pre> The average number of gallons per mile = {{{total_gallons/total_miles}}} = {{{(3*60*60 + 2*60*50)/(3*600+2*500)}}} = 6 gallons per mile. <U>ANSWER</U> </pre> <H3>Problem 7</H3>A total of 9 students donated money for a school fundraiser and their average donation was $12. If the average donation for 5 of the students was $16, what was the average donation, for the remaining for students? <B>Solution</B> <pre> If the average donation of 9 students was $12, it means that the total amount of donation of these 9 students was 9*12 = 108 dollars. Since the average donation of 5 of the students was $16, their total donation was 5*16 = 80 dollars. Hence, the total donation of remaining 4 students was 108 - 80 = 28 dollars. It means that the average donation of these 4 students was 28/4 = 7 dollars. <U>ANSWER</U> </pre> <H3>Problem 8</H3>A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 75, 82, and 74. Sara's quiz scores are 86, 72, 92, and 96. Her final examination score is 75. Use the weighted mean formula to find Sara's average for the course. (Round the answer to one decimal place.) <B>Solution</B> <pre> From the condition, four quiz scores are 86, 72, 92 and 96 with the weight coefficient of 1 each; three tests scores are 75, 82 and 74 with the weight coefficient of 2 each. final examination score is 75 with the weight of 2*2 = 4. So, the numerator is (86 + 72 + 92 + 96) + 2*(75 + 82 + 74) + 4*75 = 1108. The number of different kind of quiz/tests/examinations, in terms of quizzes, is 4 + 2*3 + 4*1 = 14. The weighted average is {{{((86 + 72 + 92 + 96) + 2*(75 + 82 + 74) + 4*75)/(4 + 2*3 + 4*1)}}} = {{{1108/14}}} = 79.1 rounded to one decimal place, as requested. <U>ANSWER</U>. Using the weighted mean formula, Sara's average for the course is 79.1, rounded to one decimal place. </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-weight-height-and-temperature.lesson>Solved problems on average scores, weight, height and temperature</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/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>
