bach1 problemas tema4

5/19/2018 Bach1 Problemas Tema4

1/5

(2n+ 1)2 + (2n+ 3)2 = 1570 = x2 + (x+ 2)2 = 1570 = x2 +x2 + 4x+ 4 = 1570 = 2x2 + 4x 1566 =

0 = x2 + 2x 783 = 0 =

x= 23136

2 =256

2 =

27

29 no valida

Dividendo= cocientedivisor+resto=

x+y = 147

x= 5y+ 9= 5y+ 9 + y = 147 = 6y= 138 = y= 23 = x=

A x= C0 (103)1

B x+ 1250 =C0 (104)1

B A= 1250 = 104 C0 103 C0 = 1250 = 001 C0 = C0 = 12

50

001 = 1250

H oy En 5 anos

Padre 4x 3 (x+ 5)

Hija x x+ 5

4x+ 5 = 3 (x+ 5) = 4x+ 5 = 3x+ 15 = x= 10

Hace 3 anos Dentro de 6 anos

Persona 1 6x 3 (x+ 9)

Persona 2 x x+ 9

6x + 9 = 3 (x+ 9) = 6x + 9 = 3x + 27 = 3x= 18 = x= 6


2/5

x+y = 32

20x+ 5y = 400=

x= 32 y

20 (32 y) + 5y = 400= 640 20y+ 5y = 400 =15y= 240 = y= 16

=

v =

AB = (100, 180)

x0100

= y32180

= x = 100y3200180

= 5y1609

x= 32 = 32 = 5y1609

= 288 = 5y 160 = 448 = 5y= y = 896

1

3

1

5

x+1

y+1 = 1

3 3x+ 3 =y + 1

x3y3 =

1

5 5x 15 =y 3

= 2x 18 = 4 = 2x= 14 = x= 7

3x+ 3 =y + 1 = 21 + 3 =y + 1 = y= 23

x

y= 7

23

25 = x12

+ x4

25 = 4x12

= 30 = 4x= x= 75

l1, l2 A1, A2 B1, B2

l1+l2 = 1000

l1= A1+B1 = 3B1+B1= 4B1

l2 =

A2+

B2=

B2+

B2 = 2

B2

=

4B1+ 2B2= 1000

B1+B2 = 400= 2B1= 200 = B1= 100

B2= 300

A1= 300 A2 = 300

l1= 400 50 = 20,000 l2= 600 60 = 36,000


3/5

cm2

P = 2x+ 2y= 50 = y = 502x

2 = 25 x= A= x (25 x)

156 = 25x x2 = x2 25x+ 156 = 0 = x= 25252411562 = 2512 = 2512 =

1312

x+y = 36

2x+y = 60= x= 24

= y= 12

x+y = 825

115x+ 095y= 86375=

115x+ 115y= 94875

115x+ 095y= 86375= 020y= 85 = y= 425 = x= 400

x+y = 35

094x+ 088y= 3140=

094x+ 094y = 3290094x+ 088y = 3140

= 006y = 150 = x= 10 = y = 25

094 10 = 940

25 088 = 22

e= v t

A x= 90 t= x= 90t

B x+ 10 = 115 t= x= 115t 10= 90t = 115t 10 = 25t = 10 = t = 10

25 = m

60 = m =

600

25 = 24


4/5

e= v t A x= 80 t

B 22 x= 100 (t 005)=

t= x

80

t= 22x100

+ 005= x

80 = 22x

100 + 005 = x

80 = 27x

100 = x

4 =

27x5

=

= 5x= 108 4x= 9x= 108 = x= 12

=

x y = 35

(x+ 2) (y 3) = 18=

x= 35

y

(x+ 2) (y 3) = 18=

35

y+ 2 (y 3) = 18 =

= 35 + 2y 105y 6 = 18 = 2y 105

y+ 11 = 0

= 2y2 + +11y 105 = 0 = y= 1131

4 =

5

105

y = 5 = x = 7

x y= 360

(x 4) (y+ 45) = 360=

x= 360

y

(x 4) (y+ 45) = 360=

360

y 4 (y+ 45) = 360

=

360

4y

+

1620

y

18 = 360 =

4y

+

1620

y

18 = 0

=

4y2

+ 18y

1620 = 0 =

2y2

+ 9y

810 = 0 =

= y= 9814

=

18

225

y = 18 = x = 20

Julia y

Clara 02 xMiguel y+ 100

02x+y = 850

y+ 02x+y+ 100 =x=

02x+y = 850

08x 2y= 100=

04x+ 2y= 1700

08x 2y= 100=

= 12x= 1800 = x= 1500

= y= 850 02 1500 = 550

Julia y 550 hojas 550 001 = 55Clara 02 x 300 hojas 300 001 = 3

Miguel y+ 100 650 hojas 650 001 = 65


5/5

z

y= 3

4= 4z 3y= 0

x+y+z = 800

10x+ 20y+ 50z= 16000

3y+ 4z= 0

=

x+y+z = 800

x+ 2y+ 5z = 1600

3y+ 4z = 0

=

x+y+z = 800

y+ 4z = 800

3y+ 4z = 0

=

x+y+z = 800

y+ 4z = 800

16z= 2400

z = 240016

= 150

= y+ 4z = 800 = y = 800 4z = 800 4 150 = 200

=

x+y+z = 800 = x= 800 y z= 800 200 150 = 450

A+B +C= 270

B+C=A+ 30

035 (A+B) =C

=

A+B+C= 270

A+B+C= 30

035 A+ 035B C= 0

=

A+B +C= 270

2B+ 2C= 300

135C= 945

= C = 945

135 = 70

2B+ 2C= 300 =

B+ C= 150 =

B = 150

C= 150

70 = 80

A+B+C= 270 = A= 270B C= 270 80 70 = 120

bach1 problemas tema4

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