A customer at a store paid $64 for 3 large candles. A second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is... A customer at a store paid $64 for 3 large candles. A second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. What are the prices of the large and small candles?
Understand the Problem
The question involves determining the prices of large and small candles based on the amounts paid by two customers. The first customer paid $64 for 3 large candles, and the second customer paid $4 more than the first for 1 large candle and 8 small candles. We need to set up equations to find the price of each size candle.
Answer
The price of a large candle is \( x = \frac{64}{3} \), and the price of a small candle is \( y = \frac{35}{6} \).
Answer for screen readers
The price of a large candle is ( x = \frac{64}{3} \approx 21.33 ) dollars, and the price of a small candle is ( y = \frac{35}{6} \approx 5.83 ) dollars.
Steps to Solve
- Define Variables
Let ( x ) be the price of a large candle and ( y ) be the price of a small candle.
- Set Up the Equation for the First Customer
The first customer paid $64 for 3 large candles. This can be expressed as: $$ 3x = 64 $$
- Solve for the Price of a Large Candle
To find ( x ), divide both sides of the equation by 3: $$ x = \frac{64}{3} \approx 21.33 $$
- Set Up the Equation for the Second Customer
The second customer paid $4 more than the first customer, which means they paid: $$ 64 + 4 = 68 $$ for 1 large candle and 8 small candles. This can be expressed as: $$ x + 8y = 68 $$
- Substitute the Value of ( x )
Now substitute ( x ) from the previous step into the equation: $$ \frac{64}{3} + 8y = 68 $$
- Solve for the Price of a Small Candle ( y )
First, isolate ( 8y ): $$ 8y = 68 - \frac{64}{3} $$ Calculate the right side. To perform the subtraction, convert 68 to a fraction: $$ 68 = \frac{204}{3} \Rightarrow 8y = \frac{204}{3} - \frac{64}{3} = \frac{140}{3} $$ Now divide by 8: $$ y = \frac{140}{3 \cdot 8} = \frac{140}{24} = \frac{35}{6} \approx 5.83 $$
The price of a large candle is ( x = \frac{64}{3} \approx 21.33 ) dollars, and the price of a small candle is ( y = \frac{35}{6} \approx 5.83 ) dollars.
More Information
The prices indicate that large candles are significantly more expensive than small ones. This situation could apply to many retail scenarios where larger quantities or sizes cost more.
Tips
- Forgetting to convert totals when dealing with fractions can lead to errors in calculation.
- Misapplying the equation setup, particularly when translating word problems into mathematical equations, can result in incorrect setups.
AI-generated content may contain errors. Please verify critical information
