MATHS...simultaneous equation

1.A string of length 23cm is cut into two parts with lengths x cm and
square x+7 cm respectively.
(a)Find the value of x
x+√(x+7)=23
√(x+7)=23－x
x+7=x^2－46x+529
x^2－47x+522=0
(x－18)(x-29)=0
x=18 or x=29(不合)

(b)The longer piece of the two parts is chosen to enclose a square.Find thearea
of the square.
(18/4)^2
=4.5^2
=20.25cm^2

2 A retailer bought a number of glasses for a total cost of $48. Two of theglasses .
were broken accidentally in the store. However, by selling each of theremaining.
glasses at $3 more than the original cost，the retailer couldstill make a total profit
of $22.
(a)How many glasses did the retailer buy?
設共買x個
(48/x+3)*(x－2)=48+22
(48+3x)(x－2)=70x
48x－96+3x^2－6x=70x
3x^2－28x－96=0
(3x+8)(x－12)=0
x=12 orx=－8/3(不合）
(b)What was the selling price of each glass?
Sol
48/x+3
=48/12+3
=7

3. A shopkeeper bought a number of glassware for a total cost of $3600.In the
frist week, he sold 60 pieces, each one at o price of $18 more than itsoriginal
cost.After that,12 pieces were broken accidentally. In the second week, he soldall
the remaining glassware , each piece at a price of $6 less than its originalcost.
On the whole , he could still make a profit of $480. What was the original costor each
Piece of glassware?
設原本單價x元/個
60*(x+18)+(3600/x－60－12)*(x－6)=3600+480
60*(x^2+18x)+(3600－72x)*(x－6)=4080x
60x^2+1080x+3600x－21600－72x^2+432x=4080x
－12x^2+1032x－21600=0
x^2－86x+1800=0
(x－36)(x－50)=0
x=36 orx=50
when x=50，3600/50=72=60+12(與題意不合)