AdamsFamily Posted September 12, 2014 Share Posted September 12, 2014 Hi. I am using Anita Harnadek's Algebra I Word Problems book from Critical Thinking Co. with my dd. We came across this problem last night, and I nor my husband could figure it out. It is as follows: A camera store owner makes a set profit on each roll of film she sells. Yesterday she sold a certain number of film. If she had sold 5 fewer but made 1c more on each, her profit on them would have been $2.80 less. If she had sold 10 more but made 1c les on each, her profit on them would have been $6.65 more. How many did she sell? What was the profit on each one? What was the total profit on them? The answer key lists the formulas and the final answers, but not how to get from the formulas to the final answers. f = the number of rolls of film sold yesterday; p = the profit ($) made on each roll of film sold yesterday; t = the total profit ($) made on the rolls of film sold yesterday; pf = t; (f-5)(p+.01)=t-2.80; (f+10)(p-.01)=t+6.65; p=.80, f =125, t=100. This problem is in a section labeled "Mixtures" with the heading" "Use Your Common Sense". :~ If any of you could help me out, I would be very appreciative! Thanks! Quote Link to comment Share on other sites More sharing options...
Arcadia Posted September 12, 2014 Share Posted September 12, 2014 pf = t(f-5)(p+.01) = t - 2.80(f+10)(p-.01) = t + 6.65 (f-5)(p+.01) = t - 2.80fp - 5p + 0.01f - 0.05 = t - 2.80 Since fp = t, t - 5p + 0.01f - 0.05 = t - 2.80 Subtract t from both sides,- 5p + 0.01f - 0.05 = - 2.80-500p + f = -275 -> equation (1) (f+10)(p-.01)= t + 6.65fp + 10p - 0.01f -0.1 = t + 6.65 Since fp = t, t + 10p - 0.01f -0.1 = t + 6.65 Subtract t from both sides,10p - 0.01f -0.1 = 6.651000p - f = 675 -> equation (2) equation (1) + equation (2)500p = 400p = 0.80 substitute p = 0.8 into equation (1)-400 + f = -275f = 125 substitute p = 0.8, f = 125 into pf = tt = 100 Quote Link to comment Share on other sites More sharing options...
AdamsFamily Posted September 13, 2014 Author Share Posted September 13, 2014 Thank you!!!! We missed substituting fp for t after using the FOIL method. Thank you very much for your help! Quote Link to comment Share on other sites More sharing options...
MarkT Posted September 13, 2014 Share Posted September 13, 2014 Avatar police here - did you take that photo yourself? :) Quote Link to comment Share on other sites More sharing options...
Arcadia Posted September 13, 2014 Share Posted September 13, 2014 Avatar police here - did you take that photo yourself? :) :lol: Fitzgerald Marine Reserve in Moss Beach, CA Took the photo while enjoying a family outing to the tide pools. My younger boy is interested in marine biology. Quote Link to comment Share on other sites More sharing options...
AdamsFamily Posted September 13, 2014 Author Share Posted September 13, 2014 Someone in my family took the picture of that owl while it was sitting on my arm! :) Quote Link to comment Share on other sites More sharing options...
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