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Create and solve a one-variable linear equation from a short context.

Write and solve a one-variable equation for equal groups

Problem
Four notebooks cost 28 dollars total. Write and solve a one-variable equation to find the cost of one notebook.
Your answer

Hint

Let n represent the cost of one notebook. Then use the fact that 4 notebooks cost 28 dollars total to write an equation.

When identical items all cost the same amount, total cost = number of items x cost per item. Here that gives 4n = 28. Then divide both sides by 4.

Solution walkthrough

01

Define the variable and write the equation

\[\text{Let}~n~\text{be}~\text{the}~\text{cost}~\text{of}~\text{one}~\text{notebook}.~\text{Then}~4n~=~28.\]

The problem says there are 4 identical notebooks with a total cost of 28 dollars. If one notebook costs n dollars, then 4 notebooks cost 4n dollars, so the equation is 4n = 28.

02

Solve for n

\[\begin{aligned} 4n~=~28 \\ n~=~7 \end{aligned}\]

Divide both sides of the equation by 4 to find the cost of one notebook. That isolates n and gives n = 7.

03

Write the answer with units

\[n~=~7~\text{dollars}\]

The variable n represents the cost of one notebook, so the answer should be written in dollars. One notebook costs 7 dollars.

04

Check the result

\[4(7)~=~28\]

Substitute 7 back into the original equation. Since 4 times 7 equals 28, the answer is correct.

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Another way

  1. You can also think of the total cost being shared equally among 4 notebooks, so compute 28 / 4 = 7. That matches the equation method.

!

Common mistake

A common mistake is to divide incorrectly or give the answer without connecting it to the variable. The equation 4n = 28 means 28 dollars is split into 4 equal notebook costs, so you must divide by 4 and state that one notebook costs 7 dollars.