Calcular x si 6/9 = x/27
Respuestas a la pregunta
Respuesta:
a) x/6 = 35/42 x = 6*35/42 = 5
b) (x+1)/8= 5/2 x+1 = 8*5/2 = 20 x = 20-1 = 19
c) 5/(x+1) = 6/(x-2) 5*( x-2) = 6*(x+1) 5x -10 = 6x+6 x = -16
d) ( x+8)/3 = (2x-2)/8 8x + 64 = 6x-6 2x = -70 x = -35
e) 9/x=x/16 x² = 9*16 = 144 x = √144 = 12 .
2) proporción geométrica :
4;10;28;70
4/10 = 28/70 4:10= 28:70
8; 20 ; 64 ; 80 .
8/20 ≠64/80 no es proporción geométrica.
2; 6 ;10; 30
2/6 = 10/30 2:6 = 10:30 1/3 = 1/3
3) a) 21*3 = 7*9 21/7 = 9/3
21 ; 7 ; 9 ; 3
b) 5*24 = 8*15
5/8 = 15/24
5 ;8 ;15 ; 24
c) 3*45 = 5*27
3/5 = 27/45
3; 5 ; 27 ; 45
4) a) 3/5 = 21/35
3/5 = 24/40
3/5 = 27 / 45
3/5 = 30 / 50
b) 4/9 = 16/36
4/9 = 20 / 45
4/9 = 24/54
4/9 = 28/63
5) a) x/y = 5/4 x+y = 27
x = 5/4y
5/4y + y = 27
9/4y = 27
y = 27*4/9
y = 12
x = 5/4*12 = 15
b) x/y = 3/9 x+y = 32
y = 3x x +3x = 32 4x = 32 x = 8 y = 32-8 = 24
c ) 18/x = 21/y y = 7/6x
x - y = 1
x - 7/6x = 1
x = 6
y = 7/6* 6 = 7
d) 24/x = 12/y x -y = 6
x = 2y 2y - y = 6 y = 6
x = 2* 6 = 12
e) x/y = 4/2 x -y = 10
x = 2y 2y - y = 10 y = 10
x = 2* 10 = 20
6) x =? y =? z =?
a) x/3 = y/5 = z/6 x + y+ z = 98
x/3 = y/5 y = 5/3x
x/3 = z/6
z = 2x
x + 5/3x + 2x = 98
14/3x = 98
x = 98*3/14 = 21
y = 5*21/3 = 35
z= 2*21 = 42 .
b) 4/x=8/y =16/z x+y+z = 35
4/x = 8/y
y = 2x
4/x = 16/z z = 4x x + 2x + 4x = 35 7x = 35 x = 5
y = 2*5 = 10
z = 4*5 = 20
c ) x/3 = y/6 = z/18 x+y+ z = 24
x/3 = y/6 y = 2x
x/3 = z/18 z = 6x
x+ 2x+ 6x = 24 x = 24/9 = 8/3
y = 2*8/3 = 16/3
z = 6* 8/3 = 16
d ) 0.4/x = 0.2 /y = 0.8/z x+y+z = 2
0.4/ x = 0.2/y x = 2y
0.2/ y = 0.8/z z = 4y 2y + y +4y = 2 7y = 2 y = 2/7
x = 2*2/7 = 4/7
z = 4*2/7 = 8/7
e) x/6 = y/3 = z/12 x+ y +z = 7
x/6 = y/3 y = x/2 x/6 = z/12 z = 2x
x+ x/2 + 2x = 7
7/2x = 7 x= 2 y = 2/2 = 1 z = 2*2 = 4
7) x/y = 3/5 x + y = 40
x = 3/5y 3/5y + y = 40 y = 40*5/8 = 25
x = 3/5 *25 = 15
25 - 15 = 10 respuesta c) 10.
8) x/y = 5/9 x+ y = 42
x = 5/9y 5/9y + y = 42 y = 27 x = 5/9*27 = 15
La edad de luis es 15 respuesta d)
9) x-y = 12 x/y = 9/6
x= 9/6y 9/6y -y = 12
y = 24
x = 9/6*24 = 36
El menor número es = 24 respuesta c)
10) x/18 = 2/3 x= 2/3*18 = 12 el menor es 12 .
11) x/y = 3/5 x + y = 40
x = 3/5y 3/5y + y = 40 8/5y = 40 y = 25 x = 15
15/25 = 22/ 32 = 3/5 es la razón respuesta a) 3/5
12) x = y +24
y/x = 3/9 x = 3y 3y = y +24 2y = 24 y = 12
La edad del hijo es : 12 respuesta d) 12 años.
13 ) x/y = 3/7 x+y = 60 y = 7x/3 x + 7x/3 = 60
10/3x = 60
x = 18 respuesta a) 18 .
14 ) x/(x+20) = 1/6
6x = x +20
5x = 20
x = 4 respuesta d ) 4 años .
15 ) x+y+z = 120 x/3 = y/5 = z/7
x/3 = y/5 x/3 = z/7
y = 5/3x z = 7/3x
x+ 5/3x + 7/3x = 120
5x = 120 x = 120/5 = 24 y = 40 z= 56
respuesta e) 56 .
16 ) x/y = 5/3 P= 64 cm Area =?
x = 5/3y 2x+2y = 64 x +y =32 ( 5/3+ 1 )y = 32 y = 12
x= 5/3*12 = 20
Area = x*y = = 20*12 = 240 cm² respuesta c) 240 cm²
17 ) (x+2 )/( x+1+4)= 3/4
4x+8 = 3x+15
x = 7 respuesta e) 7
18 ) x/y = 2/3 y = 3/2x
( x+5 )/( y + 5) = 5/7
( x + 5 )/( 3x/2+ 5 ) = 5/7
x + 5 = 15/14x +25/7
x = 20 c)
19) x + y + z = 126 x/3 = y/4 = z/7
y = 4/3x z = 7x/3 y = ?
x + 4x/3 + 7x/3 = 126
x = 27 y = 4*27/3 = 36 respuesta e) 36
20 ) x/y = 3/5 x²+ y² = 306 x =?
y = 5x/3 x²+ ( 5x/3)² = 306
x²+ 25x²/9 = 306 34x²/9 = 306 x² = 81 x =
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