Lesson 5: Represent Situations with Equations

Represent Situations with Equations

Student Summary

Writing and solving equations can help us answer questions about situations.

A scientist has 13.68 liters of oil and needs 16.05 liters for an experiment. How many more liters of oil does she need for the experiment?

We can represent this situation with the equation:

$\displaystyle 13.68 + x=16.05$

We can solve the equation by subtracting 13.68 from each side. This gives us some new equations that also represent the situation:

$\displaystyle x=16.05 - 13.68$

$\displaystyle x=2.37$

The solution $x=2.37$ means the scientist needs 2.37 more liters of oil.

Volunteers at a food pantry divide a 54-pound bag into portions that each weigh $\frac{3}{4}$ pound. How many portions can they make?

We can represent this situation with the equation:

$\displaystyle \frac34 x = 54$

We can find the value of $x$ by dividing each side by $\frac34$ . This gives us some new equations that represent the same situation:

$\displaystyle x=54\div \frac34$

$\displaystyle x=72$

The solution $x=72$ means the volunteers can make 72 portions.

Visual / Anchor Chart

Standards

Addressing

6.EE.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q; x - p = q; px = q; and x/p = q for cases in which p, q, and x are all nonnegative rational numbers.