11)
a)
Numărul 15a se divide cu 9 daca si numai daca suma cifrelor sale se imparte la 9 => suma cifrelor ∈ {9,18,27...}
a este cifră, a∈{0,1,2,....,9}
1+5+a = 9 => a = 9-6 => a = 3
15a = 153
[tex]\bf \dfrac{x}{6}= \dfrac{153}{27}[/tex]
[tex]\bf 27\cdotx = 153\cdot6[/tex]
[tex]\bf 27x = 918[/tex]
[tex]\bf x =\dfrac{918}{27}[/tex]
[tex]\bf x =\dfrac{\not918}{\not27}[/tex]
[tex]\boxed{\bf x =34}[/tex]
b)
2a - numar prim
a- este cifra => a∈ {0,1,2...,9}
dar 2a ≤ 25 => a = 3, 2a = 23 ( 23 numar prim mai mic decat 25)
[tex]\bf \dfrac{3}{46}= \dfrac{x}{23}[/tex]
[tex]\bf x\cdot46=3\cdot23[/tex]
[tex]\bf 46x=69[/tex]
[tex]\bf x=\dfrac{69}{46}[/tex]
[tex]\bf x=\dfrac{\not69}{\not46}[/tex]
[tex]\boxed{\bf x=\dfrac{3}{2}}[/tex]
f)
[tex]\bf \dfrac{x}{\dfrac{1}{3}}=\dfrac{\dfrac{7}{9}}{\dfrac{8}{3} }[/tex]
[tex]\bf \dfrac{x}{1}\cdot \dfrac{3}{1}=\dfrac{7}{9}}\cdot{\dfrac{3}{8} }[/tex]
[tex]\bf 3x=\dfrac{7}{\not9}}\cdot{\dfrac{\not 3}{8} }[/tex]
[tex]\bf 3x=\dfrac{7}{24}}[/tex]
[tex]\bf 3x \cdot 24 = 7[/tex]
[tex]\bf 72x = 7[/tex]
[tex]\boxed{\bf x = \dfrac{7}{72} }[/tex]
