Question

1. financial literacy tanisha takes a dance class that is priced as shown. the charge appears as negative on her account balance until she makes her monthly payment. a. show how to find the balance of tanishas account for dance classes during a 4 - week period in which she attends 3 classes per week. b. reason suppose the balance on tanishas account for a 2 - week period is - $100. if tanisha attended at least 1 dance class per week, how many classes could she have attended each week? explain your reasoning. c. evaluate the expression - 112.50÷(-12.50) and interpret what it could mean in this context.

Explanation:

A. Step - by - Step Format

Step1: Calculate the total number of classes

The number of weeks is \(n = 4\) and the number of classes per week is \(m=3\). The total number of classes \(N=n\times m\).
\(N = 4\times3=12\)

Step2: Calculate the account balance

The cost per class is \(C = 12.50\). The balance \(B\) (negative because it's a charge) is \(B=-C\times N\)
\(B=-12.50\times12\)

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B. Answer - Explanation Format

Let the number of classes in the first week be \(x\) and the number of classes in the second week be \(y\), where \(x\geq1\) and \(y\geq1\). The balance is \(B=-12.5(x + y)=- 100\). Then \(x + y=\frac{-100}{-12.5}=8\).
Since \(x\geq1\) and \(y\geq1\), the possible pairs \((x,y)\) are \((1,7)\),\((2,6)\),\((3,5)\),\((4,4)\),\((5,3)\),\((6,2)\),\((7,1)\)

Answer:

The possible number of classes per week pairs are \((1,7)\),\((2,6)\),\((3,5)\),\((4,4)\),\((5,3)\),\((6,2)\),\((7,1)\)

C. Step - by - Step Format

Step1: Evaluate the expression

We know that \(-112.50\div(-12.50)=\frac{-112.50}{-12.50}\)
Since \(\frac{a}{b}=\frac{\vert a\vert}{\vert b\vert}\) when \(a\) and \(b\) have the same sign. \(\vert-112.50\vert = 112.50\) and \(\vert-12.50\vert=12.50\)
\(\frac{112.50}{12.50}=\frac{1125}{125}\) (multiplying numerator and denominator by 10)
\(\frac{1125\div25}{125\div25}=\frac{45}{5} = 9\)

Step2: Interpret the result

In this context, if the balance is \(-112.50\) (a charge of \(112.50\)) and each class costs \(12.50\), then the number of classes is \(9\)