Amelia is raising money for her school dance. She has already raised some money by selling bracelets, and now she is selling boxes of cookies to raise more money. The table below shows the total amount of money Amelia will have raised after she sells 6,8,10 , or 15 boxes of cookies. Boxes of cookies sold (c) & Total money raised (boldsymbol(R)) 6 & 124 8 & 130 10 & 136 15 & 151 Complete the equation to represent the situation. [ R=square c+square ] Complete the sentences to make true statements. rate of change 106 number of boxes sold initial value 118 3 The amount of money Amelia has already raised by selling bracelets is represented by the square , which is square . The additional amount Amelia raises with each box of cookies she sells is represented by the square , which is square per box.

Let's start by understanding the problem. Amelia is selling boxes of cookies to raise money. We have a table that shows the total amount of money she has raised after selling a certain number of boxes. We need to find an equation that represents this situation.First, let's find the rate of change. The rate of change is the amount of money raised per box of cookies sold. We can find this by taking the difference in the total money raised for two different numbers of boxes sold and dividing by the difference in the number of boxes sold. For example, when 8 boxes are sold, Amelia raises $130, and when 6 boxes are sold, she raises $124. The difference in money raised is $130 - $124 = $6. The difference in boxes sold is 8 - 6 = 2. So, the rate of change is $6 / 2 = $3. This means Amelia raises $3 for each box of cookies she sells.Next, let's find the initial value. The initial value is the amount of money Amelia had raised before she started selling cookies. We can find this by subtracting the total money raised from selling 6 boxes of cookies from the amount she would have raised from selling 6 boxes at $3 per box. So, the initial value is $124 - 6 * $3 = $124 - $18 = $106. This means Amelia had already raised $106 by selling bracelets before she started selling cookies.Now we can write the equation. The total money raised (R) is equal to the rate of change ($3) times the number of boxes sold (c) plus the initial value ($106). So, the equation is:\[R = 3c + 106\]Finally, let's complete the sentences:The amount of money Amelia has already raised by selling bracelets is represented by the initial value, which is $106. The additional amount Amelia raises with each box of cookies she sells is represented by the rate of change, which is $3 per box.