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Consider the number of deluxe hamburgers is $\"\"$ , the number of large fries is $\"\"$ and the number of large coals is $\"\"$ .

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The system of equations are $\"\"$

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Multiply the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$

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Multiply the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$

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Multiply the equation $\"\"$ by $\"\"$ and add to the equation $\"\"$ to eliminate $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ in equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore,one hamburger cost is $\"\"$ , one order of fries cost is $\"\"$ and one drink cost is $\"\"$ .

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One hamburger cost is $\"\"$ , one order of fries cost is $\"\"$ and one drink cost is $\"\"$ .