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numerele a si b sunt invers proportionale cu numerele 2 si 3 determinati numerele a si b daca 4a+b=28

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Lunguanamaria95
4a+b=28
[tex] \frac{a}{b}= \frac{2}{3} [/tex]
3a=2b
a=[tex] \frac{2}{3} [/tex]b
4*[tex] \frac{2}{3} [/tex]b+b=28
[tex] \frac{8}{3} [/tex]b+b=28
[tex] \frac{8}{3} [/tex]b+[tex] \frac{3}{3} [/tex]b=28
[tex] \frac{8+3}{3} [/tex]b=28
[tex] \frac{11}{3} [/tex]b=28
b=28*[tex] \frac{3}{11} 
[tex]b= \frac{84}{11} [/tex]
a=[tex] \frac{2}{3} [/tex]*[tex] \frac{84}{11} [/tex]
a=[tex] \frac{56}{11} [/tex]
Cristinaioana2
(a;b) i.p.(2;3)
4a+b=28
a/1/2=b/1/3=K ⇔a=K/2
                            b=K/3
4K/2+K/3=28 (simplificam prima fractie cu3 si a doua cu 2 pentru a avea numitor comun )⇔
12K/6+2K/6=28
14K/6=28
14K=28x6
14K=168
K=168:14
K=12
a=12:2=6
b=12:3=4
Verificare:4x6+4=24+4=28

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