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Alex
2 years ago
13

Ana ganha 1200,00 reais em seu trabalho, se ela gastar um quinto em comida e dois terços do que sobrar em aluguel, quanto sobra,

ou falta?
Mathematics
1 answer:
lidiya [134]2 years ago
3 0

Answer:

Ana fica com a quantia de 560

Step-by-step explanation:

Dado

Ana ganha = 1200

Ela gasta um quinto com comida e dois terços do que resta com o aluguel

Valor que sobrou com Ana depois de gastar com comida e aluguel

1200 - 1/5 (1200) - 1/3 (1200)

1200 - 240 -400

1200 -640

560

Ana fica com a quantia de 560

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From the information obtained from the question, two equations can be created:
 
Let x and z be the two numbers (parts)

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z  +   x  =  15  .  .  .  . (2)

By transposing (2), make 'z' the subject of the equation
z = 15 - x  .  .  .  . (3)

By substituting (3) into equation (1) to find a value for x
\frac{1}{(15 - x)} + \frac{1}{x} = \frac{3}{10}

\frac{15}{( 15 - x ) ( x )}  =   \frac{3}{10}

3 ( - x^{2}  + 15 x )  =  150

3 x^{2}  - 45x + 150 = 0

⇒  ( x - 5 )  ( x - 10 )  = 0

∴ either ( x - 5) = 0        OR    ( x - 10 ) = 0

Thus x = 5 or x = 10

By substituting the values of x into (2) to find z

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So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.





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