Question

1. reason jeffrey purchased a card for $180 that gives him 20 visits to a new gym and includes a one - time fee for unlimited use of the sauna. after 5 visits, jeff has $123.75 left on the card, and after 11 visits, he has $74.25 left on the card. write an equation that jeffrey can use to determine the cost of each visit and the fee for the sauna use. mp.2

Explanation:

Step1: Calculate the cost per visit

Let \(x\) be the cost per visit.
The number of additional visits from \(5\) to \(11\) is \(11 - 5=6\).
The amount of money spent in these \(6\) visits is \(123.75 - 74.25 = 49.5\).
So, \(x=\frac{123.75 - 74.25}{11 - 5}=\frac{49.5}{6}=8.25\).

Step2: Calculate the one - time sauna fee

Let \(y\) be the one - time sauna fee.
We know that after \(5\) visits, the remaining money is \(123.75\).
The total cost of \(5\) visits is \(5x\).
The initial amount is \(180\). So, \(180-5x=y + 123.75\).
Substitute \(x = 8.25\) into the equation: \(180-5\times8.25=y + 123.75\).
\(180 - 41.25=y + 123.75\).
\(138.75=y + 123.75\).
\(y=138.75 - 123.75=15\).

Step3: Write the linear equation

Let \(C\) be the remaining money on the card and \(n\) be the number of visits.
The linear equation is \(C=180-(8.25n + 15)\), which simplifies to \(C=- 8.25n+165\).

Answer:

The equation is \(C=-8.25n + 165\), where \(C\) is the remaining money on the card and \(n\) is the number of visits. The cost per visit \(x = 8.25\) dollars and the one - time sauna fee \(y = 15\) dollars.