Question

Se quatro brigadeiros e nove fatias de torta custaram R$ 23,25 e seis brigadeiros mais doze fatias de torta, R$ 31,50, quais os valores de um brigadeiro e de uma fatia de torta?

Answer 1

$\displaystyle x = brigadeiro\\y = torta\\\\4x = 23,25-9y\\\\x = \frac{23,25-9y}{4}\\\\\left\{ \begin{array}{l} 4x+9y = 23,25 \\ 6x + 12y = 31,50 \end{array}\right.\\\\6x+4x+9y+12y=23,25+31,50\\10x+21y=54,75\\\\10\left(\frac{23,25-9y}{4}\right) + 21y = 54,75\\\\\frac{232,50-90y}{4} +21y=54,75\\\\\frac{232,50-90y+84y}{4}=54,75\\\\\frac{232,50-6y}{4}=54,75\\\\232,50-6y=219\\-6y = 219-232,50\\-6y=-13,5\\\\y= \frac{-13,5}{-6}\\\\y = 2,25\\\\\\4x + 9y=23,25$

$\displaystyle 4x+9(2,25)=23,25\\4x+20,25=23,25\\4x=23,25-20,25\\4x=3\\\\x=\frac{3}{4}\\\\x = 0,75$

Com isso, o valor do brigadeiro é R$ 0,75 e da torta é R$ 2,25.