A group of students had a stall in a flea market. They bought some glassware for $48, but two of them were broken accidentally. They sold each glassware at a price of $3 more than its original cost. Suppose the profit of selling all the glassware was$22.
(a) What was the number of glassware bought by the students originally?
(b) What was the selling price of each piece of glassware?
(a)答案= 12
(b)答案= $7
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超急!! F.4 Maths 文字題一題 (難度一般)
2012-09-23 1:51 am
回答 (2)
2012-09-23 7:11 am
✔ 最佳答案
Let they bought n glasses with c dollars eachSo, cn = 48, selling price = c + 3
Then (c + 3)(n - 2) - 48 = 22
cn + 3n - 2c = 76
3n - 2c = 28
3n - 2(48/n) = 28
3n^2 - 28n - 96 = 0
(3n + 8)(n - 12) = 0
n = -8/3 or 12
So, they sold 12 glasses
(b) c = 48/12 = 4
So, the selling price is c + 3 = 7 dollars
2012-09-23 2:29 am
Let the original number of glassware be n and the selling price of each piece of glassware be $x.
Then the cost of each glassware = x-3
Total cost = 48⇒ n(x-3)=48....(1)
Profit = 22⇒ (n-2)x-48=22⇒(n-2)x=70.....(2)
From (1): n=48/(x-3)...(3)
Put (3) into (2)
48/(x-3)-2]x=70
[48-2(x-3)]x=70(x-3)
x²+8x-105=0
(x+15)(x-7)=0
x=7 or x=-15 (rej)
When x=7, from (3), n=12.
Then the cost of each glassware = x-3
Total cost = 48⇒ n(x-3)=48....(1)
Profit = 22⇒ (n-2)x-48=22⇒(n-2)x=70.....(2)
From (1): n=48/(x-3)...(3)
Put (3) into (2)
48/(x-3)-2]x=70
[48-2(x-3)]x=70(x-3)
x²+8x-105=0
(x+15)(x-7)=0
x=7 or x=-15 (rej)
When x=7, from (3), n=12.
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