Given the equation $\frac{v}{8.6}=15.3$, solve for $v$.
The problem asks to solve for the variable \(v\) in the given linear equation:
\[\frac{v}{8.6} = 15.3\]
This is a basic algebraic equation where the variable \(v\) is divided by a constant, \(8.6\). To isolate \(v\), we must perform the inverse operation, which is multiplication.
To isolate \(v\), multiply both sides of the equation by \(8.6\):
\[v = 15.3 \times 8.6\]
By performing this multiplication:
\[v = 131.58\]
The value that satisfies the given equation is \(131.58\).
Imagine you are at a store and you want to calculate the total amount paid for a specific number of items when you only know the unit price and the total. For example, if you know the total cost of a bulk purchase of fruit was \$15.30 per kg and you bought 8.6 kg, you can find the total cost by multiplying the unit price by the weight. Solving simple linear equations like this allows us to determine missing values in everyday shopping, budgeting, and planning.