ice is a book seller. he purchase a book at $3 and sold it it at $8. for every 2 book that he sells to a customer, he gives the customer a free copy of the book. he made a total profit of $1235. he gave away a total of 150 books free. question is how many people bought 1 book from him.
2007-07-01 05:42:21 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
selling 2 books = $7 profit
150 x $7 = $105
$1235 - 105 = ???
take ??? / $5 .
try figuring it out.
2007-07-01 05:47:44 · answer #1 · answered by Anonymous · 0⤊ 1⤋
He gave a way 150 books so 150 people people purchase 2 books for a total of 450 books at a cost of 3*450 = 1350.
His revenue was 16 *150= 2400 so his profit was 2400 - 1350 = 1050. The remaining profit of 1235-1050= 185 came fro persons buying 1 book. Thus remaining people = 185/5= 37 people who bought 1 book.
2007-07-01 16:43:28 · answer #2 · answered by ironduke8159 7 · 1⤊ 0⤋
x = number of people who bought 2 books
y = number of people who bought 1 book
7x + 5y = 1235
(7, 5) = 1 is a divisor of 1235, so there are infinitely many solutions to this linear diophantine equation.
7(3) + 5(-4) = 1
7(3*1235) + 5(-4*1235) = 1235*1
7(3705) + 5(-4940) = 1235
A specific solution is (3705, -4940).
A general solution is(3705 + 5k , -4940 + (-7k)) where k is an integer.
If all customers bought 1 book, then there are 1235 / 5 = 247 customers who bought 1 book.
247 > or = -4940 + (-7k) > or = 0
5187 > or = -7k > or = 4950
-741 < or = k < or = -705.7
Solutions that meet the conditions of the problem:
(3705 + 5(-706), -4940 + (-7)(-706)) = (175, 2)
(3705 + 5(-707), -4940 + (-7)(-707)) = (170, 9)
(165, 16)
(160, 23)
(155, 30)
(150, 37)
pattern continues to
(3705 + 5(-741), -4940 + (-7)(-741)) = (0, 247)
So, the number of people who bought one book is -4940 + (-7)k where -705 < k < -742.
But, 150 books were given away free. 150 free books implies 150 people bought 2 books.
So, 3705 + 5k = 150
5k = -3555
k = -711
The solution to the problem is (3705 + 5(-711), -4940 + (-7)(-711)) = (150, 37)
ANSWER: 37
2007-07-01 14:11:31 · answer #3 · answered by mathjoe 3 · 1⤊ 0⤋
Let x be the number of people who bought 1 book from him.
Since there are 150 books sold free, we have
(2*150+x)(8) - (3*150+x)(3) = 1235
(income - cost = profit)
Solve for x,
x = 37
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2007-07-01 12:55:13 · answer #4 · answered by sahsjing 7 · 1⤊ 0⤋
profit,P
cost,C
Sale price,S
P=S-C however if 2S, P=2S-3C
so total profit is the sum of S-C plus the sum of (2S-3C)
P=1235, S=8, C=3
x=number of people buying 1 book
y=number of people buying 2 books
1235=x(S-C) + y(2S-3C)
1235=x(5) + y(7)
we know he gave away 150 free books so y=150
therefore
1235=5x+150(7)
185=5x
x=37
2007-07-01 12:52:50 · answer #5 · answered by theanswerman 3 · 1⤊ 0⤋
your ques seems incorrect, put it clearly
2007-07-01 12:59:23 · answer #6 · answered by Ξlectronegative™дtif® 2 · 0⤊ 2⤋