Questions: 1. Radi bi zmešali 6 litrov koktajla DAIQUIRI. Koliko sladkornega sirupa potrebujemo in koliko svetlega ruma, če imamo 4 dcl soka limete? Pojasnite postopek reševanja. 2. Koktajl bomo postregli v kozarcu, ki ga vidite na sliki. Ali lahko v kozarec z danimi merami natočimo 1 dcl pijače? Utemeljite odgovor. 3. Dve skupini prijateljev sta na zabavi naročali pijačo. Prva skupina je naročila 3 koktajle Daiquiri in 2 koktajla deviška Pina colada, za kar so odšteli 19 €. Druga skupina pa je naročila 4 koktajle Daiquiri in eno deviško Pina colado ter plačala 19,5 €. Koliko stane posamezna pijača? Reši sistem računsko, rešitev pa preveri grafično s pomočjo tehnologije.

1. Radi bi zmešali 6 litrov koktajla DAIQUIRI. Koliko sladkornega sirupa potrebujemo in koliko svetlega ruma, če imamo 4 dcl soka limete? Pojasnite postopek reševanja. 2. Koktajl bomo postregli v kozarcu, ki ga vidite na sliki. Ali lahko v kozarec z danimi merami natočimo 1 dcl pijače? Utemeljite odgovor. 3. Dve skupini prijateljev sta na zabavi naročali pijačo. Prva skupina je naročila 3 koktajle Daiquiri in 2 koktajla deviška Pina colada, za kar so odšteli 19 €. Druga skupina pa je naročila 4 koktajle Daiquiri in eno deviško Pina colado ter plačala 19,5 €. Koliko stane posamezna pijača? Reši sistem računsko, rešitev pa preveri grafično s pomočjo tehnologije.
Transcript text: 1. Radi bi zmešali 6 litrov koktajla DAIQUIRI. Koliko sladkornega sirupa potrebujemo in koliko svetlega ruma, če imamo 4 dcl soka limete? Pojasnite postopek reševanja. 2. Koktajl bomo postregli v kozarcu, ki ga vidite na sliki. Ali lahko v kozarec z danimi merami natočimo 1 dcl pijače? Utemeljite odgovor. 3. Dve skupini prijateljev sta na zabavi naročali pijačo. Prva skupina je naročila 3 koktajle Daiquiri in 2 koktajla deviška Pina colada, za kar so odšteli $19 €$. Druga skupina pa je naročila 4 koktajle Daiquiri in eno deviško Pina colado ter plačala $19,5 €$. Koliko stane posamezna pijača? Reši sistem računsko, rešitev pa preveri grafično s pomočjo tehnologije.
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Solution

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Solution Steps

Step 1: Determine the amount of each ingredient for 6 liters of Daiquiri

To make 6 liters (6000 ml) of Daiquiri with a ratio of 1:3 for sugar syrup to light rum and lime juice, we need to determine the total parts and then calculate each part.

  1. The ratio 1:3 means 1 part sugar syrup and 3 parts light rum.
  2. Total parts = 1 (sugar syrup) + 3 (light rum) = 4 parts.
  3. Each part = 6000 ml / 4 = 1500 ml.

So, we need:

  • 1500 ml of sugar syrup
  • 4500 ml of light rum (3 parts * 1500 ml)
Step 2: Verify if the given glass can hold 1 dcl of drink

The glass is a cone with a diameter of 10 cm and a height of 7 cm. We need to calculate its volume and compare it to 1 dcl (100 ml).

  1. Radius (r) = diameter / 2 = 10 cm / 2 = 5 cm.
  2. Volume of a cone (V) = (1/3) * π * r² * h
    • V = (1/3) * π * (5 cm)² * 7 cm
    • V ≈ (1/3) * π * 25 cm² * 7 cm
    • V ≈ (1/3) * π * 175 cm³
    • V ≈ 183.26 cm³ (since 1 cm³ = 1 ml, V ≈ 183.26 ml)

Since 183.26 ml > 100 ml, the glass can hold 1 dcl of drink.

Step 3: Solve the system of linear equations for the cost of each drink

We have two equations based on the given costs:

  1. 3D + 2P = 19 (where D is the cost of a Daiquiri and P is the cost of a Pina Colada)
  2. 4D + P = 19.5

To solve this system:

  1. Multiply the second equation by 2 to align the coefficients of P:

    • 8D + 2P = 39

  2. Subtract the first equation from this result:

    • (8D + 2P) - (3D + 2P) = 39 - 19
    • 5D = 20
    • D = 4

  3. Substitute D = 4 into the second equation:

    • 4(4) + P = 19.5
    • 16 + P = 19.5
    • P = 3.5

Final Answer

  • The amount of sugar syrup needed is 1500 ml, and the amount of light rum needed is 4500 ml.
  • The glass can hold 1 dcl of drink.
  • The cost of a Daiquiri is 4 €, and the cost of a Pina Colada is 3.5 €.
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