Solve for $v$ in the proportion. [tex]\frac{v}{17.6}=\frac{9}{9.6}[/tex]
Answer (2)
We have the proportion 17.6 v = 9.6 9 .
Multiply both sides by 17.6 to isolate v : v = 9.6 9 × 17.6 .
Calculate the value: v = 16.5 .
The solution is 16.5 .
Explanation
Understanding the Problem We are given the proportion 17.6 v = 9.6 9 and our goal is to solve for v . This means we want to isolate v on one side of the equation.
Isolating v To isolate v , we can multiply both sides of the equation by 17.6 . This gives us: v = 9.6 9 × 17.6
Calculating v Now, we just need to calculate the value of v . We can perform the multiplication: v = 9.6 9 × 17.6 = 9.6 158.4 = 16.5
Final Answer Therefore, the value of v is 16.5 .
Examples
Proportions are useful in everyday life. For example, if you know that 9 apples cost $9.6, you can use a proportion to find the cost of 17.6 apples, assuming the price per apple remains constant. This is a direct application of proportional reasoning, helping you make informed decisions about purchases and understand relationships between quantities.
To find v in the proportion 17.6 v = 9.6 9 , we cross-multiply and find that v = 16.5 . This is calculated by dividing the product of 9 and 17.6 by 9.6. Hence, v equals 16.5 .
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