The equation $9(u-2)+1.5 u=8.25$ models the total miles Michael traveled one afternoon while sledding, where $u$ equals the number of hours walking up a hill and $(u-2)$ equals the number of hours sledding down the hill. Which is the value of $u$?
A. $u=0.25$
B. $u=0.75$
C. $u =1.1$
D. $u=2.5
Answer (1)
Expand the equation: 9 ( u − 2 ) + 1.5 u = 9 u − 18 + 1.5 u .
Combine like terms: 10.5 u − 18 = 8.25 .
Isolate the variable: 10.5 u = 26.25 .
Solve for u : u = 10.5 26.25 = 2.5 . The value of u is 2.5 .
Explanation
Understanding the Problem We are given the equation 9 ( u − 2 ) + 1.5 u = 8.25 that models the total miles Michael traveled. Our goal is to find the value of u , which represents the number of hours Michael spent walking up the hill.
Expanding the Equation First, we need to expand the equation by distributing the 9 across the terms inside the parentheses: 9 ( u − 2 ) + 1.5 u = 8.25 9 u − 18 + 1.5 u = 8.25
Combining Like Terms Next, we combine the like terms, which are the terms containing u :
9 u + 1.5 u − 18 = 8.25 10.5 u − 18 = 8.25
Isolating the Variable Now, we want to isolate the term with u . To do this, we add 18 to both sides of the equation: 10.5 u − 18 + 18 = 8.25 + 18 10.5 u = 26.25
Solving for u Finally, to solve for u , we divide both sides of the equation by 10.5 :
u = 10.5 26.25 u = 2.5
Final Answer Therefore, the value of u is 2.5 .
Examples
Understanding how to solve linear equations like this can help you in many real-life situations. For example, if you are planning a road trip and need to calculate how long it will take to reach your destination based on your speed and the distance, you can use a similar equation. Or, if you are trying to budget your expenses and need to figure out how much you can spend each month, you can set up a linear equation to model your income and expenses.
