Chapter 3.6, Problem 1CCYP

To determine

Use the equation $\text{D}=75g$ find the amount donated for 12 goals.

Answer to Problem 1CCYP

The amount $900 will be donated for 12 goals.

Explanation of Solution

Given:

The ordered pairs are: $(1,75),(2,150),(3,225),(4,300),(5,375)$

Concept Used:

Let the amount of donation is D and number of goals g .

Calculation:

Look for the pattern that can be described in an equation.

The difference between the values of goals is + 1. The difference in values for the donation pay D (in $) is 75.

This suggests that the k − value is $k=\frac{75}{1}=75$ .

So, the equation is $\text{D}=75g$ , where D is the amount of donation and g is the number of goal.

We can check this equation by substituting values for g into the equation. $\text{D}=75g$

  $\begin{array}{l}\text{if}g=1;\text{then}\text{D}=75·1=75\\ \text{if}g=2;\text{then}\text{D}=75·2=150\\ \text{if}g=3;\text{then}\text{D}=75·3=225\\ \text{if}g=4;\text{then}\text{D}=75·4=300\end{array}$

Now use this equation $\text{D}=k·g$ to predict how much money will be donated for 12 goals.

The equation $\text{D}=75g$

  $\begin{array}{l}\text{D}=kg\\ \text{D}=75g\text{Original}\text{equation}\\ D=75·12\text{or}900g=12\\ D=900\end{array}$

$900 will be donated for 12 goals.

Thus, the amount $900 will be donated for 12 goals.