Verified answer

A = 57,1 °A

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Para estabelecermos uma relação entre duas escalas termométricas precisamos obter uma proporcionalidade entre elas, tipo uma regra de três.

No nosso caso

a) Comparando as escalas X com a escala Celsius

80 °A -----------------------> 180 °B

      A -----------------------> 120 °B

-5 °A -----------------------> 25 °B

[tex]\dfrac{A-(-5)}{80-(-5)}= \dfrac{120-25}{180-25}\\\\\\\dfrac{A+5}{80+5}= \dfrac{95}{155}\\\\\\\dfrac{A+5}{85}= \dfrac{95}{155}\\\\\\Simplifica\:os\:denominadores\:por\:5\\\\\\\dfrac{A+5}{17}= \dfrac{95}{31}\\\\\\Multiplica\:em\:cruz\\\\\\31\cdot (A+5)=17\cdot 95\\\\\\31\cdot (A+5)=1\,615\\\\\\A+5=\dfrac{1\,615}{31}\\\\\\A+5 = 52,1\\\\\\A = 52,1+5\\\\\\\mathbf{A = 57,1\:^oA}[/tex]