A community center sold regular memberships and premium memberships, collecting a total of $2,050. The relationship is modeled by the equation
How many dollars more does a premium membership cost than a regular membership?
In a total-cost equation, a coefficient is the number multiplying a count, and it gives the price of one item. Match each coefficient to the kind of membership its letter counts, then subtract the regular price from the premium price. The tempting mistake is to give one membership’s full price instead of the difference between the prices.
Hints
- Hint 1
The coefficient of a letter is the number multiplying it. In a cost equation, that number gives the price of one item of the kind the letter counts. Which letter counts regular memberships?
- Hint 2
The whole term gives the money from all premium memberships, while gives the price of one. Once you have both prices, which operation tells you how many dollars more premium costs?
Step-by-step
Read the prices, then subtract
Step 1Find the regular price
No Desmos needed. The equation’s coefficients give the prices directly. Because counts regular memberships, is the money from all regular memberships. Its coefficient, , means one regular membership costs $50. A coefficient gives the price of one; the whole term gives the money from that type.
- Step 2
Find the premium price
Because counts premium memberships, is the money from all premium memberships. So its coefficient gives the price of one premium membership: $75.
- Step 3
Find how much more premium costs
Subtract the regular price from the premium price to find how many dollars more premium costs:
A premium membership costs $25 more than a regular membership. Choice C.