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Chapter 6: Problem 59

In Exercises 59-72, solve each proportion and check. \(\frac{24}{x}=\frac{12}{7}\)

Short Answer

Expert verified
The solution to the proportion \(\frac{24}{x} = \frac{12}{7}\) is \(x=14\).

Step by step solution

01

Identify the given proportion

The given proportion is \(\frac{24}{x}=\frac{12}{7}\)
02

Use the cross-multiplication method to solve the proportion

Cross-multiplication is a shortcut method which can be used when two fractions are equal to each other, represented as a/b = c/d. The method involves multiplying a and d, and b and c and setting those two products as equal to each other, resulting in ad = bc. Therefore, from the given proportion, we can write the equation as \(x*12 = 24*7\).
03

Solve for x

Solve the equation to find the value of x by dividing both sides by 12, as follows - \(x= \frac{24*7}{12}\)
04

Calculating the result

After calculating the right-hand side of the equation, we find that \(x=14\)
05

Checking the solution

The solution can be checked by substituting x = 14 into the original proportion, and verifying if both sides are equal - \(\frac{24}{14} ?= \frac{12}{7}\).

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