Question

Sabendo que a − b = −16 , determine a e b na proporção a/ 6 = b/8

Answer 1

Resolvendo:

$\mathsf{\dfrac{a}{6}=\dfrac{b}{8}}\\\\\\\mathsf{a=\dfrac{6b}{8}}\\\\\\\mathsf{a=\dfrac{3b}{4}}$

Substituindo na primeira equação:

$\mathsf{a-b=-16}\\\\\\\mathsf{\dfrac{3b}{4}-b=-16}\\\\\\\mathsf{\dfrac{3b}{4}-\dfrac{4b}{4}=-16}\\\\\\\mathsf{\dfrac{3b-4b}{4}=-16}\\\\\\\mathsf{-\dfrac{b}{4}=-16}\\\\\\\mathsf{b=16\cdot 4}\\\\\\\boxed{\boxed{\mathsf{b=64}}}\\\\\\\\\mathsf{a-b=-16}\\\mathsf{a=b-16}\\\mathsf{a=64-16}\\\boxed{\boxed{\mathsf{a=48}}}$