Solve this problem to impress your gf!!!

Algebra Level 2

Let $f(x) = \frac{32-x}{7x+40}$ and $g(x) = \sqrt{x}$ . If $gf(a)= \frac{3}{5}$ , find $a$ .

1 solution

Noel Lo
Apr 28, 2015

$gf(a) = \frac{3}{5}$

$g(\frac{32-a}{7a+40}) = \frac{3}{5}$

$\sqrt{\frac{32-a}{7a+40}} = \frac{3}{5}$

$\frac{32-a}{7a+40} = (\frac{3}{5})^2 = \frac{9}{25}$

$25(32-a) = 9(7a+40)$

$800-25a = 63a+360$

$(63+25)a = 800 - 360$

$88a = 440$

$a= \frac{440}{88} = \boxed{5}$

What if I am the girl? Nice solution by the way.

Bloons Qoth - 4 years, 11 months ago