Christina is looking to join a gym. The sign-up fee is $24.99 and the membership is $29.98 a month. Determine how many months (m) that Christina signed up for if she paid $204.87?
The correct answer and explanation is:
To determine how many months Christina signed up for, let’s break down the problem into an equation. Christina paid a total of $204.87, which includes both a one-time sign-up fee and a monthly membership cost.
The total cost consists of:
- A sign-up fee of $24.99 (one-time charge),
- A monthly membership fee of $29.98 for each month Christina signed up for.
Let the number of months she signed up for be denoted as m. The equation representing the total cost is: Total cost=Sign-up fee+(Monthly fee×Number of months)\text{Total cost} = \text{Sign-up fee} + (\text{Monthly fee} \times \text{Number of months})
Substituting the known values into the equation: 204.87=24.99+(29.98×m)204.87 = 24.99 + (29.98 \times m)
To solve for m, start by subtracting the sign-up fee from both sides of the equation: 204.87−24.99=29.98×m204.87 – 24.99 = 29.98 \times m
This simplifies to: 179.88=29.98×m179.88 = 29.98 \times m
Now, divide both sides of the equation by 29.98 to isolate m: m=179.8829.98≈6m = \frac{179.88}{29.98} \approx 6
Thus, Christina signed up for 6 months.
Explanation:
The key steps involved are setting up the equation based on the problem’s given values and solving it step by step. The one-time sign-up fee was subtracted from the total cost to find the amount that corresponds to the membership fee over m months. Then, dividing by the monthly fee gave the number of months Christina signed up for. This approach ensures the total amount paid matches the cost breakdown, and through solving the equation, we find that the correct answer is 6 months.