Question

2. Fie numerele a şi b direct proporţionale cu 5 și 3. Se
cere:​

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{a}{5} =\frac{b}{3} \\3a=5b\\\\a=\frac{5b}{3}$

a)

$\frac{2a+b}{3b-a} =\frac{\frac{5b}{3} +b}{3b-\frac{5b}{3} }\\\frac{\frac{5b+3b}{3} }{\frac{9b-5b}{3} } = \frac{\frac{8b}{3} }{\frac{4b}{3} } = \frac{8b}{3}*\frac{3}{4b}= 2$

b)

$a+b = 160\\\frac{5b}{3} +b = 160\\5b+3b = 480\\8b=480\\b= 60\\a= \frac{5b}{3} \\a= 100$

c)

$a*b = 135\\\frac{5b}{3} *b = 135\\\frac{5b^{2} }{3} =135\\5b^{2}= 405\\b^{2}=81\\b=9\\a=\frac{5b}{3}\\a= 15\\Ma= \frac{a+b}{2} = \frac{9+15}{2} =12$