Homemade Pies Janet bakes homemade pies and sells them at...

Homemade Pies Janet bakes homemade pies and sells them at the local farmers market. Janet's weekly profit from the pies can be found using the formula $P=3.75 x-33.75$. In this equation $P$ represents the profit in dollars and $x$ represents the number of pies sold. a) Determine Janet's weekly profit if she sells 50 pies. b) How many pies would Janet have to sell in one week in order to break even $(P=0)$ ? c) How many pies would Janet have to sell in one week in order to have a profit of $\$ 300 ?$

Homemade Pies Janet bakes homemade pies and sells them at the local farmers market. Janet's weekly profit from the pies can be found using the formula $P=3.75 x-33.75$. In this equation $P$ represents the profit in dollars and $x$ represents the number of pies sold.
a) Determine Janet's weekly profit if she sells 50 pies.
b) How many pies would Janet have to sell in one week in order to break even $(P=0)$ ?
c) How many pies would Janet have to sell in one week in order to have a profit of $\$ 300 ?$

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Key Concepts

Linear Functions

A linear function represents a relationship between two variables where the change between the variables is constant. In many real-world situations, such as calculating profit, a linear function can model the relationship between cost, revenue, and other variables. The function is often written in the slope-intercept form (y = mx + b), where the slope m represents the rate of change and the intercept b represents the fixed starting value or cost.

Substitution

Substitution is the process of replacing a variable with a given number or expression in order to compute the value of an equation. In the context of the problem, the value of the variable x (number of pies sold) is replaced with a specific number to find the corresponding profit. This method is a fundamental technique in algebra for evaluating functions and testing specific cases.

Solving Linear Equations

Solving linear equations involves finding the value of the unknown variable that makes the equation true. This is typically done by isolating the variable on one side of the equation through inverse operations such as addition, subtraction, multiplication, or division. In practical applications, like determining break-even points or target profits, solving such equations allows us to determine the exact input needed to reach a particular output.

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