A coefficient is the number multiplying a variable. In a two-item sales system, one equation counts items and the other adds up revenue. Use the revenue equation to match each coefficient to the item its variable counts, then read the coefficient in dollars per item. Don't confuse that price with the revenue from all items of that kind.
Hints
- Hint 1
The two equations track different totals: one counts hats, and the other counts dollars. To interpret a number, first ask which kind of total its equation represents.
- Hint 2
A coefficient is the number multiplying a variable. In a revenue equation, the coefficient gives dollars per item, while the entire term gives dollars from all those items. Which variable is multiplied by the number you're interpreting?
Step-by-step
Read the revenue equation
Step 1Identify what each equation counts
No Desmos needed. The question asks what a number means, not for a solution to the system. The equation counts hats. The equation counts dollars, because the store's combined revenue is $258. So its terms describe money from each kind of hat.
- Step 2
Match the term to the hats
The problem says counts knit hats, so is the money from all knit hats. The multiplies the count; it isn't the number of knit hats sold.
- Step 3
Interpret the multiplier
In , each knit hat contributes dollars. So the coefficient gives the price per knit hat, while the full term gives their total revenue. Each knit hat costs $12. Choice B.