Math Problem Statement

Use the formula d = (r - c)t to find c if d = 12, r = 5, and t = 4.

Solution

You are given the formula d=(rc)td = (r - c)t and need to solve for cc using the values:

  • d=12d = 12
  • r=5r = 5
  • t=4t = 4

To isolate cc, let's rearrange the formula:

d=(rc)td = (r - c)t

First, divide both sides by tt to simplify:

dt=rc\frac{d}{t} = r - c

Next, isolate cc by subtracting rr from both sides:

c=rdtc = r - \frac{d}{t}

Now, substitute the known values:

c=5124c = 5 - \frac{12}{4}

Simplifying:

c=53=2c = 5 - 3 = 2

Thus, c=2c = 2.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to consider:

  1. How would you solve for tt in the same equation?
  2. What happens if t=0t = 0 in this formula?
  3. Can you express rr in terms of dd, cc, and tt?
  4. How would the result change if dd were negative?
  5. What does the variable cc represent in practical terms in this formula?

Tip: When solving for a variable, isolate it by performing inverse operations step by step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

d = (r - c)t

Theorems

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Suitable Grade Level

Grades 8-10