A local gym charges a monthly membership fee of 12.50 dollars plus a one-time registration… — ACT

A local gym charges a monthly membership fee of $12.50$ dollars plus a one-time registration fee of $b$ dollars. The total cost, $y$ , in dollars, for $x$ months is given by the linear equation $y = 12.50x + b$ . If a member paid a total of $100$ dollars for $6$ months of membership, what is the registration fee, $b$ , in dollars?

A
$75.00$
B
$81.50$
$25.00$ Answer
D
$175.00$
E
$37.50$

Answer

25.00

The correct answer is found by substituting the total cost of

100

for

y

and the number of months,

6

, for

x

in the equation

y = 12.50x + b

, giving

100 = 12.50(6) + b

. Multiplying

12.50

6

yields

75

, and subtracting

75

from

100

gives the registration fee

b = 25

Step-by-Step Solution

Identify and substitute the given values into the linear equation.

Substitute

y = 100

(total cost) and

x = 6

(number of months) into

y = 12.50x + b

to get

100 = 12.50(6) + b

This sets up the equation with one variable, allowing us to solve for the unknown registration fee

b

Calculate the total cost of the monthly fees.

12.50 \times 6 = 75

. The equation becomes

100 = 75 + b

We multiply the monthly fee rate by the number of months to find the portion of the total cost spent on monthly fees.

Solve for the registration fee

b

b = 100 - 75 = 25

Subtracting the total monthly fees from the total cost isolates

b

to find the registration fee.

Key Concept

Solving linear equations in slope-intercept form by substituting known values to find the y-intercept.

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