The equation \( \frac{c}{a} = r - d \) expresses a relationship between four variables: \(c\), \(a\), \(r\), and \(d\). To solve for one variable in terms of the others, you can rearrange the equation accordingly.

### Solving for \(c\):
Multiply both sides by \(a\) to isolate \(c\):
\[
c = a(r - d)
\]

### Solving for \(a\):
Divide both sides by \((r - d)\) to isolate \(a\):
\[
a = \frac{c}{r - d}
\]

### Solving for \(r\):
First, add \(d\) to both sides:
\[
\frac{c}{a} + d = r
\]

So,
\[
r = \frac{c}{a} + d
\]

### Solving for \(d\):
Subtract \(r\) from both sides and then multiply by \(-1\):
\[
d = r - \frac{c}{a}
\]

Would you like to go over a specific variable or an example? 

Here are 5 related questions:

1. What happens to \(c\) when \(r\) and \(d\) are equal?
2. How does changing \(a\) affect the value of \(r\)?
3. Can \(d\) be negative in this equation?
4. If \(r = 0\), what does that imply about the relationship between \(c\), \(a\), and \(d\)?
5. How would you solve this equation if \(r\) and \(d\) are functions of time?

**Tip:** When solving equations involving fractions, it's often useful to eliminate the fraction by multiplying both sides by the denominator, as it simplifies the equation significantly.

Explore the equation c/a = r - d and learn how to solve for variables such as c, a, r, and d. This problem involves manipulating equations with fractions and understanding relationships between variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation