At a local fitness center, members pay a $10 membership fee and $4 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
(Type in a whole number)
Let's say the number of aerobics classes is x.
For members, the cost is the membership fee plus $4 for each class:
Cost for members = $10 + $4x
For nonmembers, the cost is $5 for each class:
Cost for nonmembers = $5x
We need to find the value of x for which the cost for members and nonmembers is the same:
$10 + $4x = $5x
Rearranging the equation:
$4x - $5x = -$10
-$x = -$10
x = 10
Therefore, for 10 aerobics classes, the cost for members and nonmembers will be the same.
Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
y - x = 5
4y = 4x + 20
Let's rearrange each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First equation:
y - x = 5
Rearranging, we get: y = x + 5
Second equation:
4y = 4x + 20
Dividing both sides by 4, we get: y = x + 5
Comparing both equations, we can see that they are the same equation. The system is graphed as a single line.
This means that the system has infinitely many solutions since any point on the line satisfies both equations.