Solve for $g$ in the proportion.
[tex]\frac{172}{g}=\frac{2}{9}[/tex]
$g=\square$
Answer (1)
Cross-multiply the proportion: 172 × 9 = 2 × g .
Simplify the equation: 1548 = 2 g .
Divide both sides by 2 to solve for g : g = 2 1548 .
The solution is: 774 .
Explanation
Understanding the Problem We are given the proportion g 172 = 9 2 . Our goal is to solve for g .
Cross-Multiplication To solve for g , we can cross-multiply. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction. So we have:
172 × 9 = 2 × g
This simplifies to:
1548 = 2 g
Isolating g Now, to isolate g , we divide both sides of the equation by 2:
2 1548 = 2 2 g
This simplifies to:
g = 774
Final Answer Therefore, the value of g that satisfies the proportion is 774.
Examples
Proportions are useful in everyday life. For example, if you know that 2 apples cost 1 , yo u c an u se a p ro p or t i o n t o f in d o u t h o w m u c h 9 a ppl escos t . S e tt in gu pt h e p ro p or t i o n \frac{2}{1} = \frac{9}{x} , w h ere x i s t h ecos t o f 9 a ppl es , a ll o w syo u t oso l v e f or x$ and find the cost. This concept is widely used in cooking, scaling recipes, and calculating costs.
