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All courses Algebra I · A-CED.A.1 1 of 76
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 \(\$28\) total. Write an equation for the cost \(n\) of one notebook and solve it.
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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 unknown cost

\[n~=~\text{cost}~\text{of}~1~\text{notebook}~\text{in}~\text{dollars}\]

The prompt supplies the symbol n for the cost of one notebook. Because all four notebooks are identical, each notebook contributes the same n-dollar cost.

02

Write the equal-groups equation

\[\text{number}~\text{of}~\text{notebooks}~\times~\text{cost}~\text{per}~\text{notebook}~=~\text{total}~\text{cost};~4n~=~28\]

Total cost equals the number of equal items times the cost of one item. The prompt gives 4 notebooks and a 28-dollar total, so substituting those values gives 4n = 28.

03

Isolate the variable

\[4n~/~4~=~28~/~4;~n~=~7\]

Divide both sides by 4 because the variable is multiplied by 4. Applying the same operation to both sides preserves equality and gives n = 7.

04

Check and state the solution

\[4(7)~=~28;~4n~=~28;~n~=~7~\text{dollars}\]

Substituting 7 for n gives 28, the stated total cost. Therefore the equation and solution are 4n = 28 and n = 7 dollars, exactly matching choice A.

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Another way

  1. Share the 28-dollar total equally among four notebooks: 28 / 4 = 7 dollars per notebook.

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Common mistake

Do not subtract 4 from 28. The equation contains four equal groups of n, so undoing multiplication by 4 requires division by 4.

Solution walkthrough video