Ejercicio 88

1

las partes son a,b,c

a+b+c = 196
b = 2a
a+b = c+20

puedes reemplazar b

a + 2a + c = 196
a+2a = c +20

despejas c en la segunda

3a - 20 = c

reemplazas

3a + 3a - 20 = 196

6a = 216

a = 216/6 = 36

b = 36 * 2 = 72

36 + 72 = c + 20

108 - 20 = c = 88

88 + 36 + 72 = 196


======================================

2

a = 3b

a - 5 = 4(b-5)

reemplazamos

3b -5 = 4b - 20

15 = b

a = 15 * 3 = 45

hace 5 años

a = 40
b = 10

===================================================
3

50 t + 35 z = 16000

t = 2z + 50

reemplazas

50 (2z + 50) + 35z = 16000

100z + 2500 + 35z = 16000

135z = 13500

z = 100

t = 250

==========================================
4
x es lo que originalmente pagaban

tenemos

6x = 4(x + 2000)

6x = 4x+8000

2x = 8000

x = 4000

Entonces la casa originalmente costaba 6x = 24000

cuando se fueron los 2 tuvieron que poner 4000 + 2000 = 6000 entre los 4 para comprarla

======================================
5
a+b = 108

2a=3b+156

despejas a en la primera

a = 108 - b

reemplazas

2(108-b) = 3b + 156

216 - 2b = 3b + 156

60 = 5b

b = 12

a = 108 - 12 = 96

el doble de 96 (192) es igual al triplo de 12 (36) + 156

==========================================
6
461 = 9x + 11
450 = 9x
x = 450/9 = 50 pies
================================
7
85 - x = 4x
85 = 5x
x = 17

17 + 68(17*4) = 85

=================================
8
a - 12 = 2(b-12)
a+12 = 3(b+12)-68

despejas a en la primera

a = 2b-12

reemplazas

2b = 3b+36-68

32 = b

Hallamos a
a - 12 = 40
a = 52

dentro de 12 años

64 = 44 * 3 - 68

64 = 132-68

64 = 64

=================================
9
a es 10 centavos y b es de 5

a+b = 22
10a+5b = 185 (el valor seria 0.1a + 0.05b = 1.85, pero pues por conveniencia)

a = 22 - b

220 - 10b + 5b = 185

35 = 5b

b = 7

tiene 7 monedas de 5 centavos

a = 22 - 7 = 15

15 monedas de 10

150 + 35 = 185

=====================================
10

(x - 24)*12 = (x-27)*24

12x - 288 = 24x-648

360 = 12x

x = 30

6 * 12 = 3 * 24

72 = 72

===============
11
x es el precio del caballo

35x = 40(x - 10)

35x = 40x - 400

5x = 400

x = 80

35 caballos le costaron 2800  (80 por caballo)
40 caballos por el mismo precio costarian 70 por caballo (40*70= 2800)

====================================================
12

3a + 55 = 233 + a

2a = 178

a = 89

(89 * 3) + 55 = 233 + 89

267 + 55 = 322

322 = 322

===================================================

13

b = a+1
c = b+1
2a + 3b + 4c = 740

despejas

c = a + 1 +1

c = a + 2

reemplazas

2a + 3a + 3 + 4a + 8 = 740

9a = 729

a = 729 / 9 = 81

b = 82

c = 83

81 * 2 + 82 * 3 + 83 * 4 = 740

162 + 246 + 332 = 740

578 + 162 = 740

740 = 740

==============================

14
a - auto
c- caballo
p- pie
a + c+ p = 150

a = 3c

p = c-20

reemplazamos

3c + c + c -20 = 150

5c = 170

c = 34

p = 34 - 20 = 14

a = 34 * 3 = 102

102 + 34 + 14 = 150

116 + 34 = 150

150 = 150

=========================
15
x hijo
y hija

3x + 2y = 16500

y = x + 2000

reemplazas

3x + 2(x + 2000) = 16500

3x + 2x +4000 = 16500

5x = 16100

x = 3220

y = x + 2000 = 3420

3 * 3220 + 2*3420 = 16500

9660 + 6840 = 16500

16500 = 16500

================================
16

b = a +1

b^2 - a^2 = 31

reemplazas

(a+1)^2 - a^2 = 31

a^2 + 2a + 1 - a^2 = 31

y asi se van esos cuadrados

2a + 1 = 31

2a = 30

a = 15

b = 16

15*15 = 225

16*16 = 256

256 - 225 = 31

===========================================

17
a = 3b
b = 5c
b = c+12

puedes igualar las 2 ultimas

5c = c+12

4c = 12

c = 3

con eso ya despejas el resto

b = 3*5 = 15

a = 3 * 15 = 45

==============================================
18

a+5 = 3(b+5)
a+15 = 2(b+15)

despejas a en la primera

a = 3b + 15 - 5
a = 3b +10

reemplazas en la segunda

3b + 10 + 15 = 2b +30

3b + 25 = 2b + 30

b = 5

a = 3*5 + 10

a = 25

en 5 años

a = 30
b = 10

en 15

a = 40
b = 20

===================================
19
a lunes
b martes
c miercoles
d jueves
e viernes
f sabado

a+b+c+d+e+f = 911
b = 2a
c = 2b
d = 2c
e = d-30
f = e+10

reemplazas, como esta es larga que sea una por una

a + 2a + c+ d+ e+ f

c= 2b entonces c = 2*2a = 4a

a+ 2a + 4a +d+ +e +f = 911

d es 2c entonces 2*4a = 8a

a+2a+4a+8a+e+f = 911

e es d-30 es decir 8a - 30

a +2a + 4a + 8a + 8a -30 + f = 911

f es e + 10 es decir 8a -30 + 10 = 8a - 20

a + 2a + 4a + 8a + 8a - 30 + 8a - 20 = 911

ya puedes resolver

31a -50 = 911

31a = 961

a = 31

b = 31 * 2 = 62

c = 62 * 2 = 124

d = 124 * 2 = 248

e = 248 - 30 = 218

f = 248 - 20 = 228


31 + 62 + 124 + 248 + 218 + 228 = 911

=============================================

a - b = 18
a + b = 3(a - b)

puedes reemplazar directamente

a + b = 3 (18)

a+b = 54

despejas

a = 54 - b

y reemplazas

54 - b - b = 18

2b = 36

b = 18

a = 18 + b = 36

================================
21

a+b = 36
a - 16 = 3b

a = 36 - b

36 - b - 16 = 3b

4b = 20

b = 5
a = 31

31 - 16 = 15
5 * 3 = 15

===============================
22
a = 3b
b = 2c
(a-1) -(b-3) = 2(c+20)

Hallamos c definiendo todo en terminos de c
a = 3b = 6c

6c-1 - 2c+3 = 2(c+20)

4c +2 = 2c + 40

2c = 38

c = 19

b = 38

a = 114

113 - 35 = 78

(19 + 20) *2  = 39 * 2 = 78

===================================

23
x valor original de lo que pagaron los 5

5x = 7(x - 800)

5x = 7x - 5600

5600 = 2x

x = 2800

la tienda costo 2800 * 5 = 14000
con 7 socios hubiera costado 2000 por cada uno

==================================================

24
a caballo peor
b caballo mejor

a+b = 120
2(a+15) = b

reemplazas

a = 120 - b

2(120 - b + 15) = b

240 - 2b +30 = b

270 = 3b

b = 90

a = 120 - 90 = 30

si el caballo peor hubiera costado 30+15 = 45 el mejor hubiera costado 45*2 = 90

==========================================================
25
a+b = 160
b = 3a

a + 3a = 160

160 = 4a = 40

a tiene 40 quetzales y b 120, por lo que a ha perdido 40 quetzales

===============================================

26
a = 2b

2(a - 400) = b + 400

reemplazas

2(2b - 400) = b + 400

4b - 800 = b+400

3b = 1200

b = 400

b tenia 400 y a 800 al comenzar

=================================
27
c caballo v vaca

c = 4v

c+5 = 3(v+5)

reemplazas

4v +5 = 3v + 15

v = 10

10 vacas y 40 caballos, con 5 mas de cada una serian 15 vacas y 45 caballos

===============================================
28
a + 6+a + 12+a + 24+a
24+a = 4a

despejas la segunda

24 = 3a

a = 8

8 + 14 + 20 + 32 = 74

================================================

29
x ahorro inicial

2x -50 + 2(2x-50) - 390 = 0

2x -50 +4x-100-390 = 0

6x = 540

x =  90

================================

30

x largo
y ancho

x = 2y

(x - 6) *  (y +4) = x * y

(2y - 6)  * (y + 4) = 2y * y

2y2 + 2y -24 = 2y2

eliminas cuadrados

2y = 24

y = 12
x = 24

superficie 12*24 = 288

y+4 = 16
x - 6 = 18

18*16 = 288

======================================================
31
a-5 = 3(b-5)

a+5 = 2(b+5)

a = 3b -10

3b-5 = 2b+10

b = 15

a = 35

hace 5

a = 30
b = 10

en 5

a =40
b=20

===========================
32
(a+4) = 3(b+4)
(a-2) = 5(b-2)

a = 3b+8

3b+6 =5b-10

2b = 16

b = 8

a = 32

dentro de 4

a = 36
b = 12

hace 2

b = 6
a = 30