Chez J Posted October 26, 2012 Share Posted October 26, 2012 Rachel signed up for a frequent-flier program and received 3000 bonus miles. She earns 1300 ff miles each time she purchases a round-trip ticket. How many ff miles will she have after 5 round trips? Now, my dd created an appropriate equation - EXCEPT - she wanted to use 5 for the round trips instead of starting at 6 for "after" the 5th one. This is almost more understanding language instead of math, understanding the word "after" in the problem. These sorts of problems are what stump her. The issue is not so much math, but the nuances of language here. How do I help her work through that? What is a good source to learn and practice this? The text we use does not teach this, it merely expects the students to somehow pick it up through osmosis of a sort. Then it only has one or two chances to practice it. Quote Link to comment Share on other sites More sharing options...
kiana Posted October 26, 2012 Share Posted October 26, 2012 Rachel signed up for a frequent-flier program and received 3000 bonus miles. She earns 1300 ff miles each time she purchases a round-trip ticket. How many ff miles will she have after 5 round trips? Now, my dd created an appropriate equation - EXCEPT - she wanted to use 5 for the round trips instead of starting at 6 for "after" the 5th one. Huh, I don't understand why you'd start at 6. After five round trips, she'll have 6500(1300 per trip) and 3000 bonus for 9500. (After googling, this appears to be part of a worksheet on arithmetic sequences. You may also be supposed to write it out as a sequence, so 3000 (initial), 4300(after 1 trip), ..., 9500 (after 5 trips).) Quote Link to comment Share on other sites More sharing options...
Chez J Posted October 26, 2012 Author Share Posted October 26, 2012 Huh, I don't understand why you'd start at 6. After five round trips, she'll have 6500(1300 per trip) and 3000 bonus for 9500. (After googling, this appears to be part of a worksheet on arithmetic sequences. You may also be supposed to write it out as a sequence, so 3000 (initial), 4300(after 1 trip), ..., 9500 (after 5 trips).) Hmm. The solutions manual has them using 6 instead of 5. But, this solutions manual has had numerous errors. Maybe a better question is to ask if the manual is correct. :confused: Quote Link to comment Share on other sites More sharing options...
Chez J Posted October 26, 2012 Author Share Posted October 26, 2012 The sequence is arithmetic because the number of frequent-flyer miles will increase 1300 for each round-trip she makes. Since the number of frequent-flyer miles will increase 1300 for each round-trip, d = 1300. Since she begins with 3000 frequent-flyer miles, a 1 = 3000. Since you want to find the number of frequent-flyer miles after 5 round-trips, you need to find the 6th term of the sequence, so n = 6. a n = a 1 + (n - 1)d a 6 = 3000 + (6 - 1)1300 = 3000 + (5)1300 = 3000 + 6500 = 9500 Rachel will have 9500 frequent-flyer miles after 5 round-trips. Quote Link to comment Share on other sites More sharing options...
Gwen in VA Posted October 26, 2012 Share Posted October 26, 2012 Working through the math section of a SAT prep book is the best "math reading comprehension" work I know. The SAT math has a strong "are you reading this carefully and understanding" element to it. I'd start out with one of the easier prep books (Princeton maybe) and then move to a harder one. Quote Link to comment Share on other sites More sharing options...
creekland Posted October 26, 2012 Share Posted October 26, 2012 Both solutions are correct. The answer key is looking at this as a sequence where the first term is 1. Therefore, you are looking for the 6th term (n = 6 plugged in). The other solution (the one I would use if simply given the problem) is linear (y = 1300x + 3000) and uses 0 for the first term. In that case you are looking for the 5th term and put a 5 in for x. You are NOT looking for the 6th round trip in either case. If you need to explain where the 6 came from, do it by pairing up terms/answers and mention the 1st term being 1. If on an ACT/SAT/any test other than sequential, the linear way is an easier way to solve these problems. Quote Link to comment Share on other sites More sharing options...
kiana Posted October 26, 2012 Share Posted October 26, 2012 The sequence is arithmetic because the numberof frequent-flyer miles will increase 1300 for each round-trip she makes. Since the number of frequent-flyer miles will increase 1300 for each round-trip, d = 1300. Since she begins with 3000 frequent-flyer miles, a 1 = 3000. Since you want to find the number of frequent-flyer miles after 5 round-trips, you need to find the 6th term of the sequence, so n = 6. a n = a 1 + (n - 1)d a 6 = 3000 + (6 - 1)1300 = 3000 + (5)1300 = 3000 + 6500 = 9500 Rachel will have 9500 frequent-flyer miles after 5 round-trips. Ok. The reason you are looking for the 6th term of the sequence is because the first term (3000) is after 0 trips. I would write the sequence as a table with the first row being 'trips' (so the first row would be 0, 1, 2, 3, 4, 5) and the second row being 'ff miles'. This will help her see why she needs the 6th term. And as creekland says, noone would ever solve the problem with the formula given in the answer key, unless specifically told to use this formula. Quote Link to comment Share on other sites More sharing options...
regentrude Posted October 26, 2012 Share Posted October 26, 2012 The sequence is arithmetic because the numberof frequent-flyer miles will increase 1300 for each round-trip she makes. Since the number of frequent-flyer miles will increase 1300 for each round-trip, d = 1300. Since she begins with 3000 frequent-flyer miles, a 1 = 3000. Since you want to find the number of frequent-flyer miles after 5 round-trips, you need to find the 6th term of the sequence, so n = 6. a n = a 1 + (n - 1)d a 6 = 3000 + (6 - 1)1300 = 3000 + (5)1300 = 3000 + 6500 = 9500 Rachel will have 9500 frequent-flyer miles after 5 round-trips. Huh? Nobody in their right mind would solve the problem like this. You'd simply do 3,000+5*1,300 if the problem was stated as in the OP. Quote Link to comment Share on other sites More sharing options...
Storm Bay Posted October 26, 2012 Share Posted October 26, 2012 Hmm. The solutions manual has them using 6 instead of 5. But, this solutions manual has had numerous errors. Maybe a better question is to ask if the manual is correct. :confused: Others have already said what I would, but I'm curious as to which math program is this. Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted October 26, 2012 Share Posted October 26, 2012 (edited) nm Edited October 26, 2012 by Teachin'Mine Quote Link to comment Share on other sites More sharing options...
Chez J Posted October 26, 2012 Author Share Posted October 26, 2012 Holt McDougal Algebra I Quote Link to comment Share on other sites More sharing options...
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