Solve for $y$ in the proportion.
$\frac{y}{3}=\frac{10.2}{9}$
Answer (2)
Multiply both sides of the equation by 3: y = 3 × 9 10.2 .
Simplify the expression: y = 9 30.6 .
Calculate the value of y : y = 3.4 .
The solution is: 3.4 .
Explanation
Understanding the Problem We are given the proportion 3 y = 9 10.2 . Our goal is to solve for y . To do this, we need to isolate y on one side of the equation.
Isolating y To isolate y , we can multiply both sides of the equation by 3: y = 3 × 9 10.2 This simplifies to: y = 9 3 × 10.2 y = 9 30.6
Calculating the Value of y Now, we perform the division: y = 9 30.6 = 3.4
Final Answer Therefore, the value of y is 3.4.
Examples
Proportions are useful in everyday life. For example, if you know that 3 apples cost 4.50 , yo u c an u se a p ro p or t i o n t o f in d t h ecos t o f 5 a ppl es . S e tt in gu pt h e p ro p or t i o n \frac{3}{4.50} = \frac{5}{x} , yo u c an so l v e f or x$ to find the cost of 5 apples. This concept is also used in recipes when scaling ingredients up or down.
To solve for y in the proportion 3 y = 9 10.2 , multiply both sides by 3 to get y = 3.4 . Thus, the value of y is 3.4.
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