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Chapter 6: Problem 38

Solve. $$ \frac{15}{x}=\frac{3}{800} $$

Short Answer

Expert verified
x = 4000

Step by step solution

01

Understand the Equation

We are given the equation: \( \frac{15}{x} = \frac{3}{800} \). The goal is to solve for the variable \( x \).
02

Cross-Multiply

Cross-multiplying the fractions on both sides of the equation, we get: \( 15 \times 800 = 3 \times x \).
03

Simplify the Equation

Simplify the equation obtained from cross-multiplying: \( 12000 = 3x \).
04

Solve for x

Divide both sides of the equation by 3 to isolate \( x \): \( x = \frac{12000}{3} \).
05

Simplify the Result

Simplify the division: \( x = 4000 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cross-Multiplication
Cross-multiplication is a fundamental technique used to solve equations involving fractions. When we have an equation like \(\frac{a}{b} = \frac{c}{d}\), cross-multiplication involves multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.
This process transforms the fractional equation into a more manageable form. For instance, given \(\frac{15}{x} = \frac{3}{800}\), cross-multiplying gives us \(15 \times 800 = 3 \times x\).
By this technique, fractions are removed, making it easier to handle the equation. This method is particularly useful because it directly leads us towards the solution.
Variable Isolation
Variable isolation is the process of manipulating the equation to have the variable on one side and constants on the other. The goal is to solve for the variable by 'isolating' it.
In our problem, after simplification, we get \(12000 = 3x\). To isolate \(x\), we divide both sides by the coefficient of \(x\), which is 3 in this case.
This gives us \(x = \frac{12000}{3}\). Performing this division, the equation simplifies to \(x = 4000\).
Isolating the variable provides the final solution and confirms the value of the variable, ensuring it satisfies the original equation.

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Most popular questions from this chapter

Solve. Cameron's Garage borrows \(\$ 5600\) at \(10 \%\) for 30 days. Find (a) the amount of interest due and (b) the total amount that must be paid after 30 days.

Find the \(\mathrm{LCM}\) of 18 and 60 .

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Find the prime factorization of 90 .

If \(p\) is \(120 \%\) of \(q,\) then \(q\) is what percent of \(p ?\)
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