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Modeling with Equations and Inequalities


Videos and lessons to help High School students learn how to combine standard function types using arithmetic operations. 

For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model

Common Core: HSF-BF.A.1b

Related Topics:
Common Core (Functions)

Common Core for Mathematics

Making more pizzas to spread cost per pizza

Dominique from "Dominique's Pizza" bakes the same amount of pizza every day. She used to spend $8 each day on using the oven and $1.50 on ingredients for each pizza.

One day the prize of ingredients increased from $1.50 to $2.00 per pizza. Dominique made some calculations and found that she should bake 8 pizzas more each day so that the expenses for a single pizza would remain the same.

Write an equation to find out how many pizzas Dominique baked each day before the change in price. Use p to represent the number of pizzas.

Quadratic inequality word problem

Lisa owns a "random candy" vending machine, which is a machine that picks a candy out of an assortment in a random fashion. Lisa controls the probability in which each candy is picked.

She is running out of "honey bunny", so she wants to program its probability so the probability of getting a different candy twice in a row is is greater than 2 1/2 times the probability of getting "honey bunny" at one try.

Write an in equality that models the situation. Use p to represent the probability of getting "honey bunny" in one try.

Constructing an exponential equation example

Liam opens a savings account and put $650 in it. Each year, the account increases by 50%.

How many years would it take the account to reach $12,960?

Write an equation that models the situation. Use t to represent the number of years since Liam opened the account.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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