Question

Show that 9a + 3b has a greater value than 3x + 4y (photo provided)

Answer 1

`\bf \begin{array}lll 3a+b&=&7&&6x+8y&=&40\\&&&&&\\ 3(3a+b)&=&3(7)&&(1)/(2)(6x+8y)&=&(1)/(2)(40)\\&&&&&\\ 9a+3b&=&21&&(6x)/(2)+(8y)/(2)&=&(40)/(2)\\&&&&&\\ 9a+3b&=&21&&3x+4y&=&20 \end{array}\\\\ ~\hspace{7.5em}21>20`

Answer 2

`3a + b = 7\Leftrightarrow 3(3a + b) = 3 * 7\Leftrightarrow 9a + 3b = 21 \: (1)\\ 6x + 8y = 40\Leftrightarrow (2(3x + 4y))/(2) = (40)/(2) \Leftrightarrow 3x + 4y = 20 \: (2) \\ (1),(2)\Rightarrow 9a + 3b > 3x + 4y`