SOLUTION: 29. A bookstore can purchase several calculators for a total cost of $120. If each calculator cost $1 less, the bookstore could purchase 10 additional calculators at the same total

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Question 119997This question is from textbook Beginning and intermediate Algebra
: 29. A bookstore can purchase several calculators for a total cost of $120. If each calculator cost $1 less, the bookstore could purchase 10 additional calculators at the same total cost. How many calculators can be purchased at the regular price? This question is from textbook Beginning and intermediate Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let c = the cost of each calculator
Let n = number of calculators bought
In words:
Total cost = ( cost of each calculator ) x ( number of calculators bought )
120+=+c%2An
c+=+120%2Fn
also given is
120+=+%28c-1%29%2An+%2B+10%28c-1%29
120+=+%28c-1%29%28n%2B10%29
Substitute 120%2Fn for c
120+=+%28120%2Fn+-+1%29%28n+%2B+10%29
120+=+%28%28120-n%29%2Fn%29%2810%2Bn%29
120n+=+1200+-+10n+%2B+120n+-+n%5E2
n%5E2+%2B+10n+=+1200
complete the square
n%5E2+%2B+10n+%2B+25+=+1225
%28n%2B5%29%5E2+=+1225
n+%2B+5+=+35
n+=+30
Thirty calculators can be bought at the regular price answer
check:
120+=+%28c-1%29%2An+%2B+10%28c-1%29
120+=+%28c-1%29%2A30+%2B+10%28c-1%29
120+=+%28c-1%29%2A40
c-1+=+3
c+=+4
This says the regular price is $4
120+=+c%2An
120+=+30%2A4
120+=+120
OK