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In Bisbee, Arizona, an old mining town, you can buy souvenir nuggets of gold, silver, and bronze. For $20, you can buy any of the following mixtures of various nuggets:



(a) 14 gold, 20 silver, and 24 bronze

(b) 20 gold, 15 silver, and 19 bronze

(c) 30 gold, 5 silver, and 13 bronze



Write the Systems of Equations to represent these equations.



(There are Three answers)

14g + 15s + 13b = 20
30g + 5s + 13b = 20
5g + 13s + 20b = 30
24g + 15s + 14b = 5
20g + 15s + 19b = 20
14g + 20s + 24b = 20
30g + 15s + 24b = 20
20g + 20s + 20b = 20

Respuesta :

frika

Let g dollars be the price of gold nuggets, s dollars - the price of silver nuggets and b dollars - the price of bronze nuggets.

1)

  • If 1 gold nuggets costs $g, then 14 gold nuggets cost $14g;
  • If 1 silver nuggets costs $s, then 20 silver nuggets cost $20s;
  • If 1 bronze nuggets costs $b, then 24 bronze nuggets cost $24b.

In total they cost $20, then

14g+20s+24b=20.

2)

  • If 1 gold nuggets costs $g, then 20 gold nuggets cost $20g;
  • If 1 silver nuggets costs $s, then 15 silver nuggets cost $15s;
  • If 1 bronze nuggets costs $b, then 19 bronze nuggets cost $19b.

In total they cost $20, then

20g+15s+19b=20.

3)

  • If 1 gold nuggets costs $g, then 30 gold nuggets cost $30g;
  • If 1 silver nuggets costs $s, then 5 silver nuggets cost $5s;
  • If 1 bronze nuggets costs $b, then 13 bronze nuggets cost $13b.

In total they cost $20, then

30g+5s+13b=20.

The system of equations is

[tex]\left\{\begin{array}{l}14g+20s+24b=20\\20g+15s+19b=20\\30g+5s+13b=20\end{array}\right.[/tex]

Answer: correct equations are 2, 5 and 6

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