Question

# two year prepaid membership at gym A costs $250 for the first year plus $19 per month for the second year . A two year prepaid membership at Gym B costs $195 for the first year plus $24 per month for the second year , Leah says the cost for both gym memberships will be the same after the 11th month of the second year , Do you agree , Explain.

Hint:

### 1. Charges for 2nd year = Number of months the gym is used × charges per month.

2. Total Membership charges = Charges for 1st year + Charges for 2nd year.

## The correct answer is: the value of x for which cost of both the Gyms will be the same is @ x = 11, we disagree with the conclusion of Leah because the costs will be same for only 11 months. After 11th month the cost of Gym B will be greater than that of Gym A.

### Step-by-step solution:-

Let the number of months the gym is used in the second year be x.

From the given information, we get-

Charges of 1st year for Gym A = $ 250

Charges of 2nd year for Gym A = $ 19 per month

Charges of 1st year for Gym B = $ 195

Charges of 2nd year for Gym B = $ 24 per month

Now, we know that-

Charges of 2nd year for Gym A = Number of months of using the gym × price per month

∴ Charges of 2nd year for Gym A = x × 19 ..................................................................................... (From given information)

∴ Charges of 2nd year for Gym A = 19x ............................................................................................ (Equation i)

Total cost for gym A = Charges of 1st year + Charges of second year

∴ Total cost for gym A = 250 + 19x ....................... (From given information & Equation i) ................. (Equation ii)

Also,

Charges of 2nd year for Gym B = Number of months of using the gym × price per month

∴ Charges of 2nd year for Gym B = x × 24 ..................................................................................... (From given information)

∴ Charges of 2nd year for Gym B = 24x ............................................................................................ (Equation iii)

Total cost for gym B = Charges of 1st year + Charges of second year

∴ Total cost for gym B = 195 + 24x ....................... (From given information & Equation iii) ................. (Equation iv)

Final Answer:-

∴ Since, the value of x for which cost of both the Gyms will be the same is @ x = 11, we disagree with the conclusion of Leah because the costs will be same for only 11 months. After 11th month the cost of Gym B will be greater than that of Gym A.

A second-degree quadratic equation is an algebraic equation in x. **Ax² + bx + c = 0**, where 'x' is the variable, 'a' and 'b' are the coefficients, and 'c' is the constant term, is the quadratic equation in its standard form. A non-zero term (a ≠ 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation. The x² term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of a, b, and c are not expressed as decimals or fractions but are written as integral values. There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are referred to as the quadratic equations' roots and are given the designations (α, β). There are several ways to present the quadratic equations: (x - 1)(x + 2) = 0, 5x(x + 3) = 12x, x³ = x(x² + x - 3), where -x²= -3x + 1. Before carrying out any additional procedures, these equations are to be translated into the quadratic equation's standard form.

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