Solve the system of equations by graphing. A local fitness club has two payment options:
• Plan A: a monthly membership fee of $25, plus $2 per visit.
• Plan B: a fee of $7 per visit.
We can start by graphing both equations on the same coordinate plane. The first equation represents the total cost of Plan A as a function of the number of visits, while the second equation represents the total cost of Plan B. Let's first label the axes appropriately:
- x-axis: number of visits per month
- y-axis: total cost (in dollars)
For Plan A, the equation is:
y = 2x + 25
For Plan B, the equation is:
y = 7x
To graph these equations, we can plot a few points for each one and then connect them with a line. For Plan A, we can use the following points:
- (0, 25): no visits, only the monthly fee
- (1, 27): one visit, added $2 to the monthly fee
- (2, 29): two visits, added $4 to the monthly fee
- (5, 35): five visits, added $10 to the monthly fee
- (10, 45): ten visits, added $20 to the monthly fee
For Plan B, we can use the following points:
- (0, 0): no visits, no cost
- (1, 7): one visit, added $7 to the total cost
- (2, 14): two visits, added another $7 to the total cost
- (5, 35): five visits, added yet another $7 to the total cost
- (10, 70): ten visits, added $7 for each one
Now we can plot these points and connect them with two lines:
{insert graph here}
As we can see from the graph, the two lines intersect at the point (10, 45), which represents the number of visits for which the total cost is the same for both plans. Therefore, if someone plans to make more than 10 visits per month, Plan A is cheaper; while if they plan to make fewer, Plan B is cheaper.