Question

dois desconto secessivos de 30%e40% são equivalente a um único desconto​

Answer 1

$\Large\boxed{\begin{array}{l}\sf Vamos\,trabalhar\,com\,o\,valor\,hipot\acute etico\\\sf de\,R\ 4000,00. \\\sf no\,primeiro\,desconto\,teremos: 0,7\cdot4000=2800.\\\sf no\,segundo\,desconto\,teremos:\\\sf 0,6\cdot2800=1680.\\\sf Agora\,devemos\,encontrar\,um\,desconto\\\sf \acute unico\,de\,modo\,que\,R\ 4000,00\,se\,torne\,R\ 1680,00.\end{array}}$

$\Large\boxed{\begin{array}{l}\sf Para\,isso\,usa-se\,a\,seguinte\,equac_{\!\!,}\tilde ao:\\\sf desconto=\dfrac{valor\,antigo-valor\,novo}{valor\,antigo}\cdot100\\\\\sf desconto=\dfrac{4000-1680}{4000}\cdot100\\\\\sf desconto=\dfrac{2320}{4000}\cdot100\\\\\sf desconto=58\%\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\tt PROVA\,REAL}\\\sf fator\,de\,reduc_{\!\!,}\tilde ao=1-\%_{decimal}\\\sf fator\,de\,reduc_{\!\!,}\tilde ao=1-58\%\\\sf fator\,de\,reduc_{\!\!,}\tilde ao=1-0,58\\\sf fator\,de\,reduc_{\!\!,}\tilde ao=0,42.\\\sf Valor\,novo=valor\,antigo\cdot fator\,de\,reduc_{\!\!,}\tilde ao\\\sf Valor\,novo=4000\cdot0,42\\\sf Valor\,novo=1680\longrightarrow est\acute a\,provado.\end{array}}$