Find the unknown value in the proportion [tex]2.3 / 6.7=4.6 / x[/tex].
A. 3.4
B. 13.4
C. 1.6
D. 20.1
Answer (2)
Cross-multiply the proportion: 2.3 x = 4.6 × 6.7 .
Isolate x by dividing both sides by 2.3: x = 2.3 4.6 × 6.7 .
Simplify the expression: x = 2 × 6.7 .
Calculate the value of x : 13.4 .
Explanation
Understanding the Proportion We are given the proportion 6.7 2.3 = x 4.6 and we need to find the value of x .
Cross-Multiplication To solve for x , we can cross-multiply: 2.3 × x = 4.6 × 6.7
Isolating x Now, we isolate x by dividing both sides of the equation by 2.3: x = 2.3 4.6 × 6.7
Simplifying the Expression We can simplify the fraction by noticing that 4.6 = 2 × 2.3 , so: x = 2.3 2 × 2.3 × 6.7 = 2 × 6.7
Calculating the Value of x Finally, we calculate the value of x : x = 2 × 6.7 = 13.4
Examples
Proportions are used in everyday life to scale recipes, convert currencies, and determine distances on maps. For example, if a recipe calls for 2 cups of flour for 1 cake, you can use a proportion to find out how much flour you need for 3 cakes. Similarly, if you know the exchange rate between two currencies, you can use a proportion to convert an amount from one currency to another. Understanding proportions helps in making accurate estimations and decisions in various practical situations.
In the proportion 6.7 2.3 = x 4.6 , we find that the value of x is 13.4 after performing cross-multiplication and division. Therefore, the answer is B. 13.4.
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