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Difficulty: EasyTranslating and Solving Algebraic Word Problems

A craft shop sells handmade candles. The price of a large candle is 33 dollars more than twice the price of a small candle. If a large candle costs 1515 dollars, what is the price, in dollars, of a small candle?

Answer: 6 dollars

Answer

The price of a small candle is 66 dollars.
By letting ss represent the price of a small candle, the price of a large candle is 2s+32s + 3. Since the large candle costs 1515 dollars, we write the equation 2s+3=152s + 3 = 15. Subtracting 33 from both sides gives 2s=122s = 12, and dividing by 22 yields s=6s = 6. Therefore, the price of a small candle is 66 dollars.

Step-by-Step Solution

1
Define the variable and translate the verbal description into an algebraic expression.
Let ss be the price of a small candle. The price of a large candle is expressed as 2s+32s + 3.
Translating 'twice the price of a small candle' to 2s2s and '3 more than' to +3+ 3 allows us to represent the large candle's cost algebraically.
2
Formulate an equation by setting the expression equal to the known cost of the large candle.
2s+3=152s + 3 = 15
The problem states that the large candle costs 1515 dollars.
3
Solve the equation for the variable ss.
s=6s = 6
Subtracting 33 from both sides gives 2s=122s = 12. Dividing both sides by 22 isolates ss, resulting in 66.

Key Concept

Translating verbal statements into linear equations and solving for a single variable.

Alternative Method

We can solve the problem by working backward from the price of the large candle. Since the large candle (1515 dollars) is 33 dollars more than twice the small candle's price, we subtract 33 dollars to find twice the price of the small candle: 15−3=1215 - 3 = 12 dollars. Then, since 1212 dollars is twice the price of the small candle, we divide by 22 to find the price of a single small candle: 12÷2=612 \div 2 = 6 dollars.
Estimated Time:45s
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Topics

Translating and Solving Algebraic Word Problems

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