Math Problem Statement

c/a=r-d

Solution

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

Solving for cc:

Multiply both sides by aa to isolate cc: c=a(rd)c = a(r - d)

Solving for aa:

Divide both sides by (rd)(r - d) to isolate aa: a=crda = \frac{c}{r - d}

Solving for rr:

First, add dd to both sides: ca+d=r\frac{c}{a} + d = r

So, r=ca+dr = \frac{c}{a} + d

Solving for dd:

Subtract rr from both sides and then multiply by 1-1: d=rcad = 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 cc when rr and dd are equal?
  2. How does changing aa affect the value of rr?
  3. Can dd be negative in this equation?
  4. If r=0r = 0, what does that imply about the relationship between cc, aa, and dd?
  5. How would you solve this equation if rr and dd 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.

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Math Problem Analysis

Mathematical Concepts

Equations
Fractions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9