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# Algebraic word problems | Lesson

## What are algebraic word problems?

Algebraic word problems are questions that require translating sentences to equations, then solving those equations.
The equations we need to write will only involve
and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
On the test, there are also word problems involving two overlapping groups that we can model and solve with
.

### What skills are needed?

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

## How do we solve algebraic word problems?

Solving algebraic word problems requires us to combine our ability to create equations and solve them.
To solve an algebraic word problem:
1. Define a variable.
2. Write an equation using the variable.
3. Solve the equation.
4. If the variable is not the answer to the word problem, use the variable to calculate the answer.
It's important for us to keep in mind how we define our variables. There is often a trade-off between the complexity of what a variable represents and the complexity of the equation.

## What's a Venn diagram?

A Venn diagram is a visual representation of two or more groups and their overlap. In a Venn diagram, each circle represents a group with a
. The overlap between the circles represent members of the groups that have
. The non-overlapping part of each circle represents members of the group that have
.
Each part of the Venn diagram is related by the following equations:
\begin{aligned} A+B-\text{both}&=\text{total} \\\\ \text{only}\,A+\text{only}\,B+\text{both} &=\text{total} \\\\ \text{only}\,A &= A-\text{both} \\\\ \text{only}\,B &= B-\text{both} \end{aligned}

TRY: WRITING AND SOLVING LINEAR EQUATION
When 2 is added to the product of 6 and a certain number, the result is 20. What is the value of the number?

TRY: LINEAR EQUATION WITH REAL-WORLD CONTEXT
Eleanor bought 5 pints of frozen yogurt and a tray of jumbo shrimp from The Food Place for a total of dollar sign, 45. If the price of a tray of jumbo shrimp is dollar sign, 25, what is the price of a pint of frozen yogurt?

TRY: LINEAR EQUATION WITH REAL-WORLD CONTEXT
At Honey Beepot, the bulk price for honey is dollar sign, 2, point, 50 per pound, with a minimum purchase of 20 pounds. If Bobby paid dollar sign, 80 for some honey, by how many pounds did Bobby's purchase exceed the minimum?

TRY: MODELING WITH VENN DIAGRAM
The 22 students in Ms. Smith's 2nd grade class each have a sibling or a pet. If 14 students have a sibling and 18 students have a pet, how many students have both a sibling and a pet?
\begin{aligned} A+B-\text{both}&=\text{total} \\\\ \text{only}\,A+\text{only}\,B+\text{both} &=\text{total} \\\\ \text{only}\,A &= A-\text{both} \\\\ \text{only}\,B &= B-\text{both} \end{aligned}