Solve for x -3(x + 4) - 2 = -2(x - 5) x= -4 x = -11/5 x = 24 x = -24

Mathematics

1 answer:

Gala2k [10]4 years ago

5 0

Answer:

-24

Step-by-step explanation:

-3 (x + 4) - 2 = -2 (x - 5)

-3x - 12 - 2 = -2x + 10

-3x + 2x = 10 + 12 + 2

-x = 24

x = -24

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To fight a fire breathing dragon, a knight needs a sword made of Dragon Alloy #13, which contains 7% gold, 3% silver, and 90% ma

julia-pushkina [17]

Let $x$ and $y$ be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

$x + y = 2.7$

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$0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}$

$0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}$

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For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; $x$ kg of it will contain $0.21x$ kg of gold, $0.09x$ kg of silver, and $0.70x$ kg of steel. Each kg of magic steel of course contributes 1 kg of steel; $y$ kg of it will contribute $y$ kg of steel.

Then the dwarves need

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• total silver: $0.09x = 0.081$

• total steel: $0.70x + y = 2.43$

Solve for $x$ and $y$ . The first two equations are consistent and give $x = 0.90$ , and substituting this into the third we find $y = 1.80$ . So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.