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Zorluk: OrtaSolving One-Variable Linear Equations

A fitness center offers two membership plans. Plan A requires a one-time enrollment fee of 4545 dollars and costs 3030 dollars per month. Plan B requires a one-time enrollment fee of 105105 dollars and costs 2020 dollars per month. For how many months of membership will the total cost of both plans be exactly the same?

Cevap: 6 months

Cevap

The plans will cost the exact same amount at 6 months.
Setting the cost of Plan A (45+30m45 + 30m) equal to the cost of Plan B (105+20m105 + 20m) creates the equation 45+30m=105+20m45 + 30m = 105 + 20m. By isolating the variable, we find that 10m=6010m = 60, which simplifies to m=6m = 6. Therefore, it takes exactly 66 months for both memberships to cost the same.

Adım Adım Çözüm

1
Define the variable and formulate a one-variable linear equation.
45+30m=105+20m45 + 30m = 105 + 20m
To determine when the total costs are equal, the cost expression for Plan A (4545 fee plus 3030 per month) must be set equal to the cost expression for Plan B (105105 fee plus 2020 per month).
2
Subtract 20m20m from both sides of the equation.
45+10m=10545 + 10m = 105
This groups all terms containing the variable mm on one side of the equation.
3
Subtract 4545 from both sides of the equation.
10m=6010m = 60
This isolates the variable term by moving all constant values to the opposite side of the equation.
4
Divide both sides by 1010.
m=6m = 6
Dividing by the coefficient of the variable provides the final numerical solution for the unknown.

Anahtar Kavram

Translating a real-world scenario into a one-variable linear equation and isolating the variable to solve for an unknown value.
Tahmini Süre:1m 30s
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Konular

Solving One-Variable Linear Equations

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