Kate is selling brownies for the school bake sale. Below, you will see a chart of the number of brownies she sells and the amount of profit she earns.
Number of brownies sold | Kate’s profit
4. $8
7. $14
10. $20
13. $26
Based on the given information, we can observe that the profit Kate earns is increasing by $6 for every 3 additional brownies sold. Therefore, we can determine that Kate earns $6 for every 3 brownies sold.
To find the profit for a certain number of brownies sold, we can use the following equation:
Profit = ($6 / 3) * (Number of brownies sold - 1)
Using this equation, we can calculate the profit for other numbers of brownies sold:
For 1 brownie sold:
Profit = ($6 / 3) * (1 - 1) = $0
For 16 brownies sold:
Profit = ($6 / 3) * (16 - 1) = $30
From the given chart, we can observe that as the number of brownies sold increases, Kate's profit also increases. It appears that there is a linear relationship between the number of brownies sold and Kate's profit.
To find out how much profit Kate earns per brownie sold, we can calculate the profit per brownie by dividing the total profit by the number of brownies sold. We can choose any two data points from the chart to calculate this.
Let's take the first and second data points:
Number of brownies sold: 4
Profit: $8
Number of brownies sold: 7
Profit: $14
Change in profit = $14 - $8 = $6
Change in the number of brownies sold = 7 - 4 = 3
Profit per brownie = Change in profit / Change in number of brownies sold
Profit per brownie = $6 / 3 = $2
Therefore, Kate earns a profit of $2 per brownie sold.
Now, let's find the equation for Kate's profit based on the number of brownies sold. We can use the slope-intercept form of a linear equation, y = mx + b, where y is the profit, x is the number of brownies sold, m is the profit per brownie, and b is the y-intercept (profit when no brownies are sold).
Using any data point from the chart, we can substitute the values into the equation to find the y-intercept:
Using the first data point (4, $8):
8 = 4 * m + b
Substituting the profit per brownie, m = $2:
8 = 4 * 2 + b
8 = 8 + b
b = 0
Therefore, the equation for Kate's profit based on the number of brownies sold is:
y = 2x + 0
y = 2x
This equation shows that Kate's profit is directly proportional to the number of brownies sold.
To find the profit per brownie, we need to divide the total profit by the number of brownies sold.
Let's take the first set of data:
Kate sold 4 brownies and earned a profit of $8. To find the profit per brownie, we divide the profit by the number of brownies: $8 / 4 = $2.
Now let's apply the same calculations to the rest of the data:
For 7 brownies sold and a profit of $14: $14 / 7 = $2.
For 10 brownies sold and a profit of $20: $20 / 10 = $2.
For 13 brownies sold and a profit of $26: $26 / 13 = $2.
From all the calculations, we can see that Kate earns a profit of $2 per brownie she sells.
Therefore, the profit per brownie for Kate is $2.