Răspuns:
a) x+y+z=260
2,5,6, invers proporționale
z×x=5×y=6×z=k
x=k/2
y=k/5
z=k/6
x+y+z=k/2+k/5+k/6=260
15k/30+6k/30+5k/30=260=26k/30=260=26k =260×30=k =260×30/26=
k=300
x=300/2
x=150
y=300/5
y=60
z=300/6
z=50
b)x+y+z=790
3,5,8,-invers proporționale
)x/1/3=y/1/5=z/1/8=3x=5y=8z
3x=5y=8z
3x=k=x=k/3
5y=k=y = k/5
8z=k= z= k/8
k/3+k/5+k/8=790
numitor comun 120
40k+24k+15k÷120=790
79k=790×120
79k=94800
k=94800÷79
k,=1200
k/3=1200÷3
x= 400
y=1200÷5
y=240
z=1200÷8
z=150
d) x+y+z=1420
3,5,7 invers proporționale
x=k/3
y=k/5
z=k/7
k/3+k/5+k/7=1420
numitor comun 105
35k+21k+15k=1420
71k/105=1420
k=105×1420÷71
k=105×20
k=2100
x=k/3=2100÷3
x=700
y=k/5=2100÷5
y=420
z=k/7 = 2100÷7
z= 300