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 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
 
 
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 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
 
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 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
 
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 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
 
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 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
 
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 6
 461 = 9x + 11
 450 = 9x
 x = 450/9 = 50 pies
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 7
 85 - x = 4x
 85 = 5x
 x = 17
 
 17 + 68(17*4) = 85
 
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 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
 
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 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
 
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 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)
 
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 12
 
 3a + 55 = 233 + a
 
 2a = 178
 
 a = 89
 
 (89 * 3) + 55 = 233 + 89
 
 267 + 55 = 322
 
 322 = 322
 
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 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
 
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 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
 
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 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
 
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 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
+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
 
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 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
 
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 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
 
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 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
 
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 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