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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:
$\begin{array}{rl}A+B-\text{both}& =\text{total}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}A+\text{only}\phantom{\rule{0.167em}{0ex}}B+\text{both}& =\text{total}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}A& =A-\text{both}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}B& =B-\text{both}\end{array}$

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 $\mathrm{}45$. If the price of a tray of jumbo shrimp is $\mathrm{}25$, 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 $\mathrm{}2.50$ per pound, with a minimum purchase of $20$ pounds. If Bobby paid $\mathrm{}80$ 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 $2$nd 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?

Things to remember

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.
For a Venn diagram:
$\begin{array}{rl}A+B-\text{both}& =\text{total}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}A+\text{only}\phantom{\rule{0.167em}{0ex}}B+\text{both}& =\text{total}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}A& =A-\text{both}\\ \\ \text{only}\phantom{\rule{0.167em}{0ex}}B& =B-\text{both}\end{array}$

Want to join the conversation?

• if the world is spinning why is the sky so clear.
• and the clouds do not spin. Mother Earth is the only one that spins by herself.
• Class trip 314 students go to the museum some students pay regular price at $35 and some students get a discount and pay$21.50. The class trip cost a total of $10,072, how many students get the discounted price of$21.50
• r = students w/ regular price
d = students w/ discounted price
35r + 21.5d = 10,072
314 = r + d
314 - r = d
Therefore we can substitute d in the first equation:
35r + 21.5(314 - r) = 10,072
35r + 6751 - 21.5r = 10,072
35r - 21.5r + 6751 = 10,072
13.5r + 6751 = 10,072
13.5r = 10,072 - 6751
13.5r = 3321
r = 3321/13.5
r = 255
So now we know how many bought regular price tickets, let's use the second equation to find # of discount price students.
314 - r = d
314 - 255 = d
59 = d
Welcome.
• How do we know that the person who invented Mathematics was correct
• why is it called venn diagram?
• because it is named after the person who invented it.
John Venn
• My daughter has asked for help with the following word problem.
Dan has $1.55. The sum of dimes and nickels he has to make up$1.55 is 23. How many dimes and how many nickels does he have?
Can you help me?