A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, 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. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

Question

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, 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. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

Show your work.

Answer 1

Let's assume the price of each large candle is x dollars and the price of each small candle is y dollars.

For the first customer who bought 3 large candles and 4 small candles, the total cost can be calculated as:
3x (for 3 large candles) + 4y (for 4 small candles) = 64 ------- (Equation 1)

For the second customer who bought 1 large candle and 8 small candles, the total cost can be calculated as:
1x (for 1 large candle) + 8y (for 8 small candles) = 64 + 4 ------- (Equation 2)

We add 4 to the total cost of the second customer because it states that they paid $4 more than the first customer.

So, the system of equations that can be used to find the price of each large candle (x) and each small candle (y) is:

Equation 1: 3x + 4y = 64
Equation 2: x + 8y = 68

Now, we can solve this system of equations to find the values of x and y.