Question

Știind că 2a/(supra)9b=0,2(7), aflați valoarea raportului 8a+5b/9a-5b.
Mulțumesc anticipat! :)

Answer 1

$\frac{2a}{9b}=0,2(7)~adica~ \frac{2a}{9b}= \frac{25}{100}=\ \textgreater \ 9b\cdot25=2a\cdot100 \\ 225b=200a=\ \textgreater \ b= \frac{200a}{225} \\ \\ \frac{8a+5b}{9a-5b}= \frac{8a+5\cdot \frac{200a}{225} }{9a-5\cdot \frac{200a}{225} }= \frac{225/8a+ \frac{1000a}{225} }{225/9a- \frac{1000a}{225} }= \frac{ \frac{1800a+1000a}{225} }{ \frac{2025a-1000a}{225} }= \frac{ \frac{2800a}{225} }{ \frac{1025a}{225} }= \frac{2800a}{1025a}= \frac{2800}{1025} \\ ~simplificam~cu~25~si~obtinem~ \frac{112}{41}$