Question

aflati numerele a,b,c stiind ca;
a) sunt invers proportionale cu 2,3,5 iar suma lor este 124.
b)sunt invers proportionale cu 8 ,3, 5, iar diferenta dintre cel mare si cel mic este 75.
c)sunt invers proportionale cu 0,25;0,(3) si 0,2 iar produsul lor este 7500

Answer 1

a)
x/(1/2)=2x=k      x=k/2
y/(1/3)=3y=k      y=k/3
z/(1/5)=5z=k      z=k/5
x+y+z=124
k/2+k/3+k/5=124
15k+10k+6k=3720
31k=3720
k=120
x=k/2=120/2=60
y=k/3=120/3=40
z=k/5=120/5=24

b)
x/(1/8)=8x=k      x=k/8
y/(1/3)=3y=k      y=k/3
z/(1/5)=5z=k      z=k/5
y-x=75
k/3-k/8=75
8k-3k=1800
5k=1800
k=360
x=k/8=360/8=45
y=k/3=360/3=120
z=k/5=360/5=72

c)0,25=25/100=1/4
0,(3)=3/9=1/3
0,2=2/10=1/5
x/(1/1/4)=k   x/4=k  x=4k
y/(1/1/3)=k   y/3=k  x=3k
z/(1/1/5)=k   z/5=k  x=5k
x+y+z=7500
4k×3k×5k=7500
60k³=7500
k³=125
k=5
x=4k=4*5=20
y=3k=3*5=15
z=5k=5*5=25