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viktelen [127]
3 years ago
7

Answer questions below ASAP 5-1/2x=5/8x+2

Mathematics
1 answer:
jeka57 [31]3 years ago
5 0
Answer:   x = 8/3 ; or, write as:  2 2/3; or, write as, 2.66666667 .
_________________________________________________________
Explanation:
_________________________________________________________

 Given:   5 − 1/2 x = 5/8 x + 2 ;
______________________________________________________
    Change the  1/2 x  to "4/8 x" ;
_________________________________________________
Since "1/2" = "(1*4)/(2*4)" = "(4/8)"; and rewrite:
_________________________________________________
      → 5 − (4/8)x = (5/8)x + 2 ;
_________________________________________________
  Subtract "5"; and add "(5/8)x" to EACH side of the equation:
________________________________________________
 5 − (4/8)x  −  5 + (5/8)x  =  (5/8)x  + 2 − 5 + (5/8)x ;
_________________________________________________
to get:
_______________________________________
                 (1/8) x = (10/8)x  − 3
___________________________________________________________
Multiply the entire equation (BOTH SIDES) by "8"; to get rid of the fraction:
_________________________________________________________

8 * { (1/8) x = (10/8)x − 3 }; 
______________________________
     to get:
______________________________
              x = 10x − 24 ;
___________________________________
Subtract "x" ; and add "24" ; to EACH side of the equation:
____________________________________________________
       →      x − x + 24 =  10x − 24  − x  + 24 ;
____________________________________________________
       to get:
_____________________________________________________
            →  24  = 9x ; ↔  9x = 24 ;
______________________________________
  → Divide EACH side of the equation by "9" ; to isolate "x" on one side of the equation; and to solve for "x" ;
_______________________________________
        → 9x / 9 = 24 / 9 ;
_______________________________________
        →    x = 24/9 = (24÷3)/ (9÷3) = 8/3
_______________________________________________
        →    x = 8/3 ; or, write as:  2 2/3; or, write as, 2.66666667.
_______________________________________________________
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Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliv
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Answer:

1 litro de leche cuesta 2.5

1 kg de jamón serrano cuesta 35

1 litro de aceite de oliva cuesta 7,5

Step-by-step explanation:

Pregunta correcta completa

Un cliente de un supermercado ha pagado un total de 240 por 16 litros de leche,4kg de hamon serrano y 8 litros de aceite de oliva. Sabiendo que 1 litro de aceite cuesta el tripe de 1 litro de leche; que 1kg de jamon cuesta igual que el cliente tendria que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva. Calcule el precio de cada artículo.

Solución

Deje que el precio de un litro de leche, un kilogramo de jamón serrano y un litro de aceite de oliva sea x, y y z respectivamente.

16 litros de leche, 4 kg de hamon serrano y 8 litros de aceite de oliva cuestan 240

16x + 4y + 8z = 240 (ecuación 1)

1 litro de aceite cuesta el triple de 1 litro de leche

z = 3x (ecuación 2)

Y ese 1 kg de jamón cuesta lo mismo que el cliente tendría que pagar si hubiera comprado 5 litros de leche y 3 litros de aceite de oliva.

y = 5x + 3z (ecuación 3)

Sustituyendo las ecuaciones 2 y 3 en la ecuación 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recordemos que z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

English Translation

A supermarket customer has paid a total of 240 for 16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil. Knowing that 1 liter of oil costs the tripe of 1 liter of milk; t that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil. Calculate the price of each item.

Solution

Let the price of a liter of milk, a kilogram of Serrano ham and a liter of olive oil be x, y and z respectively.

16 liters of milk, 4kg of hamon serrano and 8 liters of olive oil cost 240

16x + 4y + 8z = 240 (eqn 1)

1 liter of oil costs the triple of 1 liter of milk

z = 3x (eqn 2)

And that 1kg of ham costs the same as the customer would have to pay if he had bought 5 liters of milk and 3 liters of olive oil

y = 5x + 3z (eqn 3)

Substituting eqn 2 and 3 into eqn 1

16x + 4(5x + 3z) + 8(3x) = 240

16x + 20x + 12z + 24x = 240

Recall that z = 3x

36x + 12(3x) + 24x = 240

36x + 36x + 24x = 240

96x = 240

x = (240/96) = 2.5

z = 3x = 3 × 2.5 = 7.5

y = 5x + 3z = (5×2.5) + (3×7.5) = 35

1 liter of milk costs 2.5

1 kg of Serrano ham costs 35

1 liter of olive oil costs 7.5

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