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pentagon [3]
3 years ago
9

Manuel se ha gastado 2/8 partes de la paga en ropa y 1/12 parte en dulces. ¿Qué fracción de la paga le queda?, ¿Si le dieron 45€

de paga, cuanto ha gastado y cuanto le queda?.
Mathematics
1 answer:
Sindrei [870]3 years ago
8 0

Responder:

2/3; 30 €

Explicación paso a paso:

Fracción gastada en ropa = 2/8

Fracción gastada en dulces = 1/12

Fracción restante:

1 - (Fracción gastada en ropa + fracción gastada en dulces)

1 - (2/8 + 1/12)

L. C. M de 8 y 12 = 24

1 - (6 + 2) / 24

1 - 8/24

1 - 1/3

= (3 - 1) / 3

= 2/3

Si la paga era de 45;

Cantidad restante: 2/3 de 45

= 90/3

= 30 €

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katovenus [111]
  1. The revenue as a function of x is equal to -x²/20 + 920x.
  2. The profit as a function of x is equal to -x²/20 + 840x - 6000.
  3. The value of x which maximizes profit is 8,400 and the maximum profit is $3,522,000.
  4. The price to be charged to maximize profit is $500.

<h3>How to express the revenue as a function of x?</h3>

Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.

Mathematically, the revenue can be calculated by using the following expression:

R(x) = x × P(x)

Revenue, R(x) = x(-1/20(x) + 920)

Revenue, R(x) = x(-x/20 + 920)

Revenue, R(x) = -x²/20 + 920x.

Expressing the profit as a function of x, we have:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = -x²/20 + 920x - (80x + 6000)

P(x) = -x²/20 + 840x - 6000.

For the value of x which maximizes profit, we would differentiate the profit function with respect to x:

P(x) = -x²/20 + 840x - 6000

P'(x) = -x/10 + 840

x/10 = 840

x = 840 × 10

x = 8,400.

For the maximum profit, we have:

P(x) = -x²/20 + 840x - 6000

P(8400) = -(8400)²/20 + 840(8400) - 6000

P(8400) = -3,528,000 + 7,056,000 - 6000

P(8400) = $3,522,000.

Lastly, we would calculate the price to be charged in order to maximize profit is given by:

P(x) = -1/20(x) + 920

P(x) = -1/20(8400) + 920

P(x) = -420 + 920

P(x) = $500.

Read more on maximized profit here: brainly.com/question/13800671

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