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? 4y = 3x + 64 8y = x + 68 4y = 3x + 64 8y = x + 60 3x + 4y = 64 x + 8y = 60

Explanation:

Step1: Analyze first customer's purchase

The first customer bought 3 large candles (each costing \( x \)) and 4 small candles (each costing \( y \)) and paid $64. So the total cost is \( 3x + 4y = 64 \).

Step2: Analyze second customer's purchase

The second customer paid $4 more than the first, so they paid LXI0? Wait, no, wait. Wait, the second customer paid $4 more than the first, so the amount is \( 64 + 4 = 68 \)? Wait, no, let's re - read. Wait, the second customer paid $4 more than the first for 1 large candle and 8 small candles. The first customer paid $64, so the second paid \( 64 + 4=68 \)? Wait, no, wait the equations in the options: Wait, let's check the third option. Wait, the third option has \( x + 8y = 60 \). Wait, maybe I made a mistake. Wait, the first customer: 3 large (\( x \)) and 4 small (\( y \)): \( 3x + 4y = 64 \). The second customer: 1 large (\( x \)) and 8 small (\( y \)), and paid $4 more than the first. The first paid $64, so the second paid \( 64 + 4 = 68 \)? But the third option has \( x + 8y = 60 \). Wait, maybe the second customer paid $4 more than the first, but maybe I miscalculated. Wait, no, let's check the options again. Wait, the third option: LXI11 (first equation) and LXI12. Wait, maybe the second customer paid LXI13? Wait, the problem says "a second customer paid $4 more than the first customer for 1 large candle and 8 small candles". Wait, no, "paid $4 more than the first customer for 1 large candle and 8 small candles" – so the amount is \( 64 + 4 = 68 \), but the third option has \( x + 8y = 60 \). Wait, maybe there's a typo in my reading. Wait, let's check the equations:

First equation for first customer: \( 3x + 4y = 64 \) (correct for 3 large and 4 small).

Second customer: 1 large (\( x \)) and 8 small (\( y \)), and the amount is \( 64 + 4=68 \)? But the third option has \( x + 8y = 60 \). Wait, maybe the problem was "paid $4 less"? No, the problem says "paid $4 more". Wait, maybe I made a mistake. Wait, let's check the options:

Option 1: \( 4y = 3x + 64 \) and \( 8y = x + 68 \) – incorrect, because the first equation should be \( 3x + 4y = 64 \), not \( 4y=3x + 64 \) (which would be \( 4y-3x = 64 \), wrong).

Option 2: \( 4y = 3x + 64 \) and \( 8y = x + 60 \) – also wrong, same as above.

Option 3: \( 3x + 4y = 64 \) (correct for first customer) and \( x + 8y = 60 \). Wait, maybe the second customer paid \( 64 - 4 = 60 \). Maybe the problem was "paid $4 less" – but the problem says "paid $4 more". Wait, maybe a misstatement. But among the options, the only one with the correct first equation (\( 3x + 4y = 64 \)) is the third option. So the system is \( 3x + 4y = 64 \) and \( x + 8y = 60 \).

Answer:

The system of equations is \(

$$\begin{cases}3x + 4y = 64\\x + 8y = 60\end{cases}$$

\), which corresponds to the third option (the one with \( 3x + 4y = 64 \) and \( x + 8y = 60 \)).