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Algebra / Linear equations in one variable Difficulty: Medium

A candle is made of $17$ ounces of wax. When the candle is burning, the amount of wax in the candle decreases by $1$ ounce every $4$ hours. If $6$ ounces of wax remain in this candle, for how many hours has it been burning?

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Explanation

Choice D is correct. It’s given that the candle starts with $17$ ounces of wax and has $6$ ounces of wax remaining after a period of time has passed. The amount of wax the candle has lost during the time period can be found by subtracting the remaining amount of wax from the amount of wax the candle was made of, which yields $17 minus 6$ ounces, or $11$ ounces. This means the candle loses $11$ ounces of wax during that period of time. It’s given that the amount of wax decreases by $1$ ounce every $4$ hours. If $h$ represents the number of hours the candle has been burning, it follows that $\frac{1}{4} = \frac{11}{h}$ . Multiplying both sides of this equation by $4 h$ yields $h equals 44$ . Therefore, the candle has been burning for $44$ hours.

Choice A is incorrect and may result from using the equation $\frac{1}{4} = \frac{h}{11}$ rather than $\frac{1}{4} = \frac{11}{h}$ to represent the situation, and then rounding to the nearest whole number.

Choice B is incorrect. This is the amount of wax, in ounces, remaining in the candle, not the number of hours it has been burning.

Choice C is incorrect and may result from using the equation $\frac{1}{4} = \frac{6}{h}$ rather than $\frac{1}{4} = \frac{11}{h}$ to represent the situation.