Question

lesson 4 | session 2
3 tiana uses the equation ( c = 21h ) to figure out the total amount, ( c ), she should charge a customer for babysitting for ( h ) hours.
a. what is the constant of proportionality? what does it mean?
b. tiana charges $94.50 for a job. how long did she babysit for? show your work.

Explanation:

Part a

Step1: Recall Proportionality Formula

The general form of a proportional relationship is \( c = kh \), where \( k \) is the constant of proportionality. In the given equation \( c = 21h \), we can compare it to the general form.

Step2: Identify the Constant

By comparing \( c = 21h \) with \( c = kh \), we see that \( k = 21 \). This constant means that Tiana charges $21 per hour for babysitting (since \( c \) is the total charge and \( h \) is the number of hours, the coefficient of \( h \) is the hourly rate).

Step1: Start with the Given Equation

We know the equation for the total charge is \( c = 21h \), and we are given that \( c = 94.50 \). We need to solve for \( h \).

Step2: Substitute and Solve for \( h \)

Substitute \( c = 94.50 \) into the equation: \( 94.50 = 21h \). To solve for \( h \), divide both sides of the equation by 21: \( h=\frac{94.50}{21} \). Calculating the right - hand side, \( \frac{94.50}{21}=4.5 \).

Answer:

The constant of proportionality is 21. It means Tiana charges $21 per hour for babysitting.

Part b