8. Word Problems: Build the Equation

GED® algebra often hides the equation in a real situation. Translate slowly.

Routine:

• Define the variable.
• Write what each part means.
• Build the equation.
• Solve.
• Check whether the answer makes sense in the story.

Example 1:
"A gym charges a 25 dollar sign-up fee plus 8 dollars per class. The total is 89 dollars. How many classes?"

Let \(c\) be the number of classes:
\[ 25 + 8c = 89. \]
Subtract 25:
\[ 8c=64. \]
Divide by 8:
\[ c=8. \]

Example 2:
"A taxi costs 4 dollars plus 2.50 dollars per mile. The total is 24 dollars. How many miles?"
\[ 4 + 2.50m = 24. \]
Subtract 4:
\[ 2.50m=20. \]
Divide by 2.50:
\[ m=8. \]

Example 3:
"Three times a number plus 5 is 41."
\[ 3x+5=41. \]
Subtract 5:
\[ 3x=36. \]
Divide by 3:
\[ x=12. \]

Common mistake: forgetting the fixed starting amount. In the gym example, 25 dollars is charged once, not once per class.