A one-variable equation can describe two kinds of items when their counts add to a known total. Use the given meaning of to find the other count, then multiply each count by its own profit per item and add the profits. Don't use for both kinds, and don't confuse a count of candles with a dollar amount.
Hints
- Hint 1
A variable represents one particular amount: here, counts only small candles. Since the 400 candles include both sizes, how many large candles are left after the small ones?
- Hint 2
A unit rate is the profit from one candle. Multiply each size's per-candle profit by its own count. What expression gives the small-candle profit, and what expression gives the large-candle profit?
- Hint 3
An equation sets two quantities equal. Your two expressions both represent dollar profits, so add them and set their sum equal to the profit target, not the total number of candles.
Step-by-step
Build the profit equation
Step 1Find the large-candle count
No Desmos needed. You're choosing an equation from the story, not solving one. The 400 candles include both sizes, and counts the small ones. Subtract the small candles to get the large-candle count: . The other group's count is the total minus the group counted by .
- Step 2
Write the small-candle profit
Each small candle brings in $1.20 in profit. Multiply that profit per candle by small candles: . This expression is in dollars.
- Step 3
Write the large-candle profit
Each large candle brings in $2.80 in profit. Multiply by the large candles: . Using would give the large candles the small-candle count.
- Step 4
Set the total profit equal to the target
The two profits must add to exactly $640, so . The right side is dollars, not the -candle count. This equation determines how many small candles the campaign sells. Choice D.