Question

fundraising natalia and her friends held a bake sale to benefit a local charity. the friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. they collected $60 on the first day and $88 on the second day. write an equation to represent the amount r natalia and her friends raised after selling c cakes.

Explanation:

Step1: Find the price per cake (slope)

First, calculate the price per cake using the two days' data. The slope \( m \) (price per cake) is calculated as \( m=\frac{\text{Change in } R}{\text{Change in } c} \). The change in \( R \) is \( 88 - 60 = 28 \), and the change in \( c \) is \( 22 - 15 = 7 \). So \( m=\frac{28}{7}=4 \).

Step2: Find the equation using point - slope form

We can use the point - slope form of a linear equation \( y - y_1=m(x - x_1) \). Let's use the first day's data: \( c_1 = 15 \), \( R_1 = 60 \), and \( m = 4 \).
Substitute into the formula: \( R-60 = 4(c - 15) \)
Expand the right - hand side: \( R-60=4c-60 \)
Add 60 to both sides of the equation: \( R = 4c \)

We can also verify with the second day's data. If \( c = 22 \), then \( R=4\times22 = 88 \), which matches the given data.

Answer:

\( R = 4c \)