Question

Seja a+b+c=92 e a,b e c são diretamente proporcionais a 1/2,2/3 e 3/4.

Determine o valor de a, b e c

Answer 1

x/2 +2x/3 +3x/4 = 92 ===> *(12) mmc
6x +8x + 9x =12*92
23x = 12*92
x =12*92/23 = 12*4 = 48

a=x/2 = 48/2= 24
b=2x/3 = 2.48/3=2.16=32
c=3x/4 = 3.48/4= 3.12=36

Answer 2

então:

$\frac{a}{ \frac{1}{2} } + \frac{b}{ \frac{2}{3} } + \frac{c}{ \frac{3}{4} } = \frac{92}{ \frac{1}{2} + \frac{2}{3} + \frac{3}{4} } \\ \\ \frac{a}{ \frac{1}{2} } + \frac{b}{ \frac{2}{3} } + \frac{c}{ \frac{3}{4} } = \frac{92}{ \frac{23}{12} } \\ \\ \frac{a}{ \frac{1}{2} } + \frac{b}{ \frac{2}{3} } + \frac{c}{ \frac{3}{4} } = 92 \times \frac{12}{23} \\ \\ \frac{a}{ \frac{1}{2} } + \frac{b}{ \frac{2}{3} } + \frac{c}{ \frac{3}{4} } = 48$

Então

resolvendo para a, temos:

$\frac{a}{ \frac{1}{2} } =48 \\ \\ a = 48 \times \frac{1}{2} = 24$

resolvendo para b, temos:

$\frac{b}{ \frac{2}{3} }=48 \\ \\ b = 48 \times \frac{2}{3} = 32$

por fim, resolvendo para c:

$\frac{c}{ \frac{3}{4} } =48 \\ \\ c = 48 \times \frac{3}{4} = 36$