Question 5 • FL-1200700-Mathematics for College Algebra MIS
Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
Answer
A
One gym charges $75 per month.
B
Each gym charges $75 per month.
C
Both gyms charge the same monthly rate and the same membership fee.
D
Both gyms charge the same monthly rate, but not the same membership fee.
Explanation
The equation 75 = 75 is always true, so the system has infinitely many solutions rather than one unique solution. This means the two gyms’ cost equations represent the same line: they have the same monthly rate and the same one-time membership fee. Therefore, Lian can conclude that both gyms charge the same monthly rate and the same membership fee.
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