Solve for the variable in [tex]7 / 28=25 / x[/tex].
A) 20
B) 100
C) 5
D) 4
Answer (2)
Cross-multiply the given proportion: 7 x = 28 × 25 .
Simplify the equation: 7 x = 700 .
Divide both sides by 7 to solve for x : x = 7 700 .
Determine the value of x : 100 .
Explanation
Understanding the Problem We are given the equation 28 7 = x 25 and asked to solve for x . This is a proportion problem, where we can find the unknown value x by cross-multiplication.
Cross-Multiplication To solve for x , we cross-multiply: 7 × x = 28 × 25 This simplifies to: 7 x = 700
Isolating x Now, we divide both sides of the equation by 7 to isolate x : 7 7 x = 7 700 This simplifies to: x = 100
Finding the Value of x Therefore, the value of x is 100.
Examples
Proportions are useful in everyday life. For example, if you know that 7 out of 28 apples in a basket are ripe, you can use a proportion to determine how many ripe apples you would expect in a larger basket of, say, 250 apples, assuming the ratio of ripe apples remains the same. This helps in estimating quantities and making informed decisions based on known ratios.
The solution to the equation 28 7 = x 25 is obtained through cross-multiplication, resulting in x = 100 . Therefore, the correct answer is 100. This demonstrates how to solve for a variable in a proportion effectively.
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