Question

4. Dacă 3ab + 5ab=846, atunci determinaţi valoarea expresiei a+b.​

Answer 1

$\displaystyle{\overline{3ab}=300 + 10a + b}$

$\displaystyle{ \overline{5ab} = 500 + 10a + b}$

$\displaystyle{ \overline{3ab} + \overline{5ab} = 846 \leftrightarrow 300 + 10a + b + 500 + 10a + b = 846}$

$\displaystyle{ 800 + 20a + 2b = 846}$

$\displaystyle{ 20a + 2b = 846 - 800 = 46}$

$\displaystyle{2 \cdot (10 a + b) = 46 \rightarrow 10a + b = 46 : 2 = 23}$

$\displaystyle{10 a + b = 23 \rightarrow a = 2, \ b = 3}$

$\displaystyle{ a + b = 2 + 3}$

$\boxed{ a + b = 5}$

- Lumberjack25

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