Question

a) nr a,b sunt direct proportionale cu 3 si 5. Daca 3a+2b=38, atunci determinati nr a si b
b) nr a,b sunt invers proportionale cu 2 si 3. Daca 6a+9b=36, atunci determinati nr a si b

Answer 1

a)
a=3k
b=5k
3a+2b=38
3kx3+5kx2=38
9k+10k=38
19k=38
k=38:19
k=2
a=2x3=6
b=2x5=10
b)
ax2=bx3=k
ax2=k⇒k=a:2
bx3=k⇒k=b:3
6a+9b=36
6k:2+9k:3=36
3k+3k=36
6k=36
k=36:6
k=6
a=6:2=3
b=6:3=2

Answer 2

a. a/3=b/5=k;
⇒a=3k; b=5k;
3a+2b=38⇒3·3k+2·5k=9k+10k=19k⇒19k=38⇒k=2;
⇒a=3·2=6;
⇒b=5·2=10;
b. a·2=b·3=k
⇒a=k/2; b=k/3;
6a+9b=36⇒se reduce la 3⇒2a+3b=12⇒2·k/2+3·k/3=12⇒k+k=12⇒2k=12⇒k=6;
⇒a=6/2=3;
⇒b=6/3=2;