At a farmers market, a vendor sells small jars of honey for $6 each and large jars for $10 each. She sells 4 fewer small jars than twice the number of large jars she sells. If her total revenue from the jars is $284, which equation could be used to find ?
A one-variable revenue equation fits a story with two products, linked counts, and one total earned. Write the second count using the given variable, then multiply each price by its own product’s count. Add those dollar amounts and set them equal to the total. Watch “fewer than”: the subtraction changes a count, not a price.
Hints
- Hint 1
The phrase 4 fewer than twice describes a jar count. Start with , then subtract . Does that give the number of small jars or large jars?
- Hint 2
A unit price is the price for one jar. Multiply each size’s price by the number of jars of that size. Which count goes with the $6 price?
- Hint 3
Revenue means money earned from sales. Add the two dollar amounts and set their sum equal to the total. A jar count by itself can’t be added to dollars.
Step-by-step
Build the revenue equation
Step 1Write the small-jar count
No Desmos needed. The question asks for the equation, not its solution.
counts large jars, so twice that count is . Four fewer means subtract , giving the number of small jars:
Adding would mean four more.
- Step 2
Find the large-jar revenue
Revenue is money earned from sales, so multiply each price by the count of its own jar size. The large jars cost $10 each, and she sells of them. Their revenue is
- Step 3
Find the small-jar revenue
The small jars cost $6 each, and she sells of them. Their revenue is
The parentheses keep the whole small-jar count together.
- Step 4
Match the total revenue
Both revenue amounts are in dollars, so add them and set the sum equal to the $284 total:
That equation can be used to find , the number of large jars. Choice C.