A school fundraiser sells small candles for $5 each and large candles for $12 each.
Which equation represents this situation, where is the number of small candles sold and is the number of large candles sold, if the total amount collected was $186?
A two-variable linear equation can describe two kinds of sales that add to one total. Multiply each price per item by the letter counting that item, then add the two dollar amounts. Match each price to the right letter before choosing an equation: swapping prices or leaving one out changes what the terms mean.
Hints
- Hint 1
A term is one part of a sum. The small-candle term must show dollars earned, not merely the number of small candles. Which price should multiply ?
- Hint 2
The letter counts large candles, not dollars. Multiply it by the price of one large candle to find how much money those candles brought in.
- Hint 3
Both sizes contribute to the same collection, so add their dollar amounts. What total should that sum equal?
Step-by-step
Build the total from each candle size
Step 1Find the small-candle amount
No Desmos needed. You're building an equation from prices and counts. Each small candle sells for $5, and counts small candles, so multiply price by count: . This term is the dollars collected from small candles.
- Step 2
Find the large-candle amount
Each large candle sells for $12, and counts large candles, so its dollar amount is . Using alone would count candles rather than the money they brought in.
- Step 3
Match the amount collected
Add the money from both sizes to match the $186 collected: . This equation represents the fundraiser's total. Choice D.