Question

Fie a si b doua numere reale direct proportionale cu 2 si 5 Calculati 5a-b stind ca 2a+b =44

Answer 1

[tex](a,b)\ direct\ proportional\ (2,5)\Rightarrow \dfrac{a}{2}=\dfrac{b}{5}=k\Rightarrow a=2k,b=5k\\ 2a+b=44\\ 4k+5k=44\\ 9k=44\\ k=\dfrac{44}{9}\\ a=2k\Rightarrow a=\dfrac{88}{9}\\ b=5k\Rightarrow b=\dfrac{220}{9}\\ 5a-b=5\cdot \dfrac{88}{9}-\dfrac{220}{9}=\dfrac{440}{9}-\dfrac{220}{9}=\dfrac{220}{9}[/tex]