Question

Sia sells large candles for $3 each and small candles for $2 each. She sold 17 candles for $46.00. How many of each size candle did she sell?

Answer 1

Let's denote the number of large candles sold as \( x \) and the number of small candles sold as \( y \).

We have two equations based on the information given:

1. The total number of candles sold:
\[
x + y = 17
\]

2. The total revenue from the candles sold:
\[
3x + 2y = 46
\]

Now we can solve this system of equations. First, we can solve the first equation for \( y \):
\[
y = 17 - x
\]

Next, we substitute \( y \) in the second equation:
\[
3x + 2(17 - x) = 46
\]

Simplifying the equation:
\[
3x + 34 - 2x = 46
\]
\[
x + 34 = 46
\]
\[
x = 46 - 34
\]
\[
x = 12
\]

Now that we have \( x = 12 \), we can find \( y \):
\[
y = 17 - x = 17 - 12 = 5
\]

Thus, Sia sold:
- Large candles: \( x = 12 \)
- Small candles: \( y = 5 \)

In conclusion, Sia sold **12 large candles and 5 small candles**.