Răspuns:
x/5=y/6=15/z=k
x=k/5
y=k/6
z=k/15
3x-2y-z=12
3·k/5-2·k/6-k/15=12
³⁾3k/5-⁵⁾k/3-k/15=¹⁵⁾12
9k-5k-k=180
k=180:3=>k=60
x=60:5=>x=12
y=60:6=>y=10
z=60:15=>z=4
__________
a/3=b/5=c/9=d/15=k
a=k/3
b=k/5
c=k/9
d=k/15
2a-3b+c-d=5
2·k/3-3·k/5+k/9-k/15=5
¹⁵⁾2k/3-⁹⁾3k/5+⁵⁾k/9-³⁾k/15=⁴⁵⁾5
30k-27k+5k-3k=225
5k=225=>k=225:5=>k=45
a=45:3=>a=15
b=45/5=>b=9
c=45/9=>c=5
d=45/15=>d=3
____________
x/4=y/5=z/6=t/10=k
x=k/4
y=k/5
z=k/6
t=k/10
2(x+y)-5z+t=10
2(⁵⁾k/4+⁴⁾k/5)-5k/6+k/10=10
2·9k/20-5k/6+k/10=10
³⁾18k/20-¹⁰⁾5k/6+⁶⁾k/10=⁶⁰⁾10
54k-50k+6k=600
10k=600=>k=600:10=>k=60
x=60/4=>x=15
y=60/5=>y=12
z=60/6=>z=10
t=60/10=>t=6
