Writing Equations from Word Problems

Front

What is the equation for a situation where a service charges a flat fee plus a variable rate per hour?

Back

y = mx + b, where m is the rate per hour and b is the flat fee.

Front

How do you represent the total cost of buying x items at a fixed price plus a one-time fee?

Back

Total Cost = (Price per item * x) + One-time fee.

Front

What does the variable 'x' typically represent in word problems involving cost?

Back

The variable 'x' usually represents the quantity of items or people.

Front

In the equation y = mx + b, what do 'm' and 'b' represent?

Back

'm' is the slope (rate of change), and 'b' is the y-intercept (fixed cost or starting value).

Front

How can you set up an equation for a total cost that includes a delivery fee?

Back

Total Cost = Delivery Fee + (Cost per item * Number of items).

Front

What is the first step in translating a word problem into an equation?

Back

Identify the quantities involved and what you need to find.

Front

If a problem states that one quantity is a certain amount more than another, how can you express this mathematically?

Back

If x is the smaller quantity, then the larger quantity can be expressed as x + amount.

Front

What is the equation for a situation where two quantities add up to a total?

Back

x + y = Total, where x and y are the two quantities.

Front

How do you determine the total cost from a word problem involving multiple items with different prices?

Back

Set up an equation that sums the costs of each item based on their quantities.

Front

What does it mean if an equation has a variable on both sides?

Back

It means you need to isolate the variable to solve for its value.