1.Mr Chan makes and sells metallic balls. The budget for making the balls is ＄7200.
If he reduces the cost of production by ＄2 each, then he can make 40 more balls.
Suppose the selling price of a ball is ＄25 and all the balls are sold out.
(a) Find the original cost of producing a ball.
(b) How many balls can he produce after reducing the production cost?
(c) Find the percentage increase of the profit.
2.Solve the equation 9^x - 4(3^x) + 3 = 0.
F4 math problems ( Circles )
2007-07-09 5:46 am
回答 (2)
2007-07-09 6:05 am
✔ 最佳答案
a)let x be original number of balls
7200/x - 2 = 7200/(x + 40)
3600(x + 40) - (x + 40)x = 3600x
x^2 + 40x - 144000 = 0
x = 360 or -400 (rejected)
original cost = 7200/360 = 20
b)
360 + 40 = 400
c)
original profit = (360)(25) - 7200 = 1800
new profit = (400)(25) - 7200 = 2800
percentage increase = (2800 - 1800)/1800*100% = 55.56%
2)
9^x - 4(3^x) + 3 = 0
(3^x)^2 - 4(3^x) + 3 = 0
(3^x - 1)(3^x - 3) = 0
3^x = 1 or 3^x = 3
x = 0 or x = 1
2007-07-09 6:13 am
1a) let x be the original cost of producing a ball
ie the original no. of ball produced = 7200/x
( 7200/ x )(x-2) + 40(x-2) = 7200
7200 - (14400/x ) + 40x - 80 =7200
7200x - 14400 + 40x^2 -80x = 7200x
40x^2 - 80x - 14400 = 0
x^2 - 2x - 360 = 0
(x+18) (x-20) =0
x= -18 (rejected) or x= 20
hence, the original cost of producing a ball =$ 20
1b)
no. of ball he can produced = $7200 / $18 = 400
1c)
the origianl profit= $(25-20)x (7200/20) = $1800
the new profit = $(25-18)x 400 = $2800
i.e the % increase of the profit= $(2800 -1800)/ $1800 x 100% = 55.56%
( corr to 2 d.p.)
2.)
9^x -4(3^x) + 3 =0
(3^x)^2 - 4(3^x) +3=0
(3^x-3)(3^x-1)=0
i.e. 3^x =3 or 3^x=1
hence x=1 or x=0
ie the original no. of ball produced = 7200/x
( 7200/ x )(x-2) + 40(x-2) = 7200
7200 - (14400/x ) + 40x - 80 =7200
7200x - 14400 + 40x^2 -80x = 7200x
40x^2 - 80x - 14400 = 0
x^2 - 2x - 360 = 0
(x+18) (x-20) =0
x= -18 (rejected) or x= 20
hence, the original cost of producing a ball =$ 20
1b)
no. of ball he can produced = $7200 / $18 = 400
1c)
the origianl profit= $(25-20)x (7200/20) = $1800
the new profit = $(25-18)x 400 = $2800
i.e the % increase of the profit= $(2800 -1800)/ $1800 x 100% = 55.56%
( corr to 2 d.p.)
2.)
9^x -4(3^x) + 3 =0
(3^x)^2 - 4(3^x) +3=0
(3^x-3)(3^x-1)=0
i.e. 3^x =3 or 3^x=1
hence x=1 or x=0
收錄日期: 2021-04-18 22:39:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070708000051KK04313