Find $34n = 1001/2$.
Answer (1)
Multiply both sides of the equation by 2: 68 n = 1001 .
Divide both sides by 68 to isolate n : n = 68 1001 .
Simplify the fraction (if possible). In this case, it's already in simplest form.
The value of n is: 68 1001 .
Explanation
Understanding the Problem We are given the equation 34 n = 2 1001 and we want to find the value of n .
Eliminating the Fraction To solve for n , we need to isolate n on one side of the equation. We can do this by multiplying both sides of the equation by 2 to eliminate the fraction: 2 ⋅ 34 n = 2 ⋅ 2 1001 68 n = 1001
Isolating n Now, we can isolate n by dividing both sides of the equation by 68: 68 68 n = 68 1001 n = 68 1001
Simplifying the Fraction To simplify the fraction, we can find the greatest common divisor (GCD) of 1001 and 68. Since the GCD is 1, the fraction is already in its simplest form. We can express this as a decimal: n = 68 1001 ≈ 14.7206
Final Answer Therefore, the value of n is 68 1001 .
Examples
Understanding how to solve for a variable in an equation is crucial in many real-life scenarios. For example, if you are trying to determine how many hours you need to work to earn a specific amount of money, you can set up an equation where the hourly rate multiplied by the number of hours equals the total amount you want to earn. Solving for the number of hours will tell you exactly how long you need to work. This concept is also used in calculating distances, determining ingredient quantities in recipes, and many other practical applications.
