Everyone knows how to find an average, but the power of this formula is often underestimated.\u00a0 We know:<\/p>\n
average = (sum of the items)\/(number of items)<\/p>\n
Notice, we can also write this as:<\/p>\n
sum of items = (average)*(number of items)<\/p>\n
This latter form can be powerful.\u00a0 For example, if we add or subtract one item from a set, we can easily figure out how that changes the sum, and that can allow us to calculate the new average.\u00a0 Also, if we are combining two groups of different sizes, we can’t add averages, but we can add sums.<\/p>\n
<\/p>\n
1) There are 17 students in a certain class.\u00a0 On the day the test was given, Taqeesha was absent.\u00a0 The other 16 students took the test, and their average was 77.\u00a0 The next day, Taqeesha took the test, and with her grade included, the new average is 78.\u00a0 What is Taqeesha’s grade on the test?<\/p>\n
(A) 78<\/p>\n
(B) 80<\/p>\n
(C) 87<\/p>\n
(D) 91<\/p>\n
(E) 94<\/p>\n
<\/p>\n
2) A company has 15 managers and 75 associates.\u00a0 The 15 managers have an average salary of $120,000.\u00a0 The 75 associates have an average salary of $30,000.\u00a0 What is the average salary for the company?<\/p>\n
(A) $35,000<\/p>\n
(B) $45,000<\/p>\n
(C) $55,000<\/p>\n
(D) $65,000<\/p>\n
(E) $75,000<\/p>\n
1) The average of the first 16 students is 77.\u00a0 This means, the sum of these 16 scores is<\/p>\n
sum = (average)*(number of scores) = 77*16 = 1232<\/p>\n
Once Taqeesha takes her test, the average of all 17 scores is 78.\u00a0 This means, the sum of these 17 scores is:<\/p>\n
sum = (average)*(number of scores) =78*17 = 1326<\/p>\n
Once we had the sum of the 16 scores, all we had to do was add Taqeesha’s score to that total to get the sum of all 17.\u00a0 Therefore, the difference in these two sums is Taqeesha’s score.\u00a0 1326 \u2013 1232 = 94.<\/p>\n
Answer: E.<\/strong><\/p>\n <\/p>\n <\/p>\n 2) The 15 managers have an average salary of $120,000. The sum of their salaries is:<\/p>\n sum = (average)*(number of salaries) = $120,000*15 = $1,800,000<\/p>\n The 75 associates have an average salary of $30,000. The sum of their salaries is:<\/p>\n sum = (average)*(number of salaries) = $30,000*75 = $2,250,000<\/p>\n When we add those two sums, we get the total payroll of all 90 employees.<\/p>\n $1,800,000 + $2,250,000 = $4,050,000<\/p>\n So, we have 90 employees, and together they earn $4,050,000, so the average is<\/p>\n average = $4,050,000 \u00f790 = $45,000<\/p>\n Answer: B.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Everyone knows how to find an average, but the power of this formula is often underestimated.\u00a0 We know: average = (sum of the items)\/(number of items) Notice, we can also write this as: sum of items = (average)*(number of items) This latter form can be powerful.\u00a0 For example, if we add or subtract one item […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[112],"tags":[],"ppma_author":[13209],"class_list":["post-378","post","type-post","status-publish","format-standard","hentry","category-math"],"acf":[],"yoast_head":"\n