Question

Q = d / d+ n on a manufacturer's assembly line, d parts are found to be defective and n parts are nondefective. the formula above is used to calculate a quality-of-parts ratio. What is d expressed in terms of the other two variables?

a. n / 1 - q
b. nq / 1 - q
c. n / q-1
d. nq / q-1

Answer 1

d. nq / q - 1

General Formulas and Concepts:

Pre-Algebra

• Equality Properties

Algebra I

• Factoring

Explanation:

Step 1: Define

q = d / (d + n)

Step 2: Solve for d

1. Multiply (d + n) on both sides: q(d + n) = d
2. Distribute q: dq + qn = d
3. Subtract qn on both sides: dq = d - qn
4. Subtract d on both sides: dq - d = -qn
5. Factor GCF: d(q - 1) = -qn
6. Divide (q - 1) on both sides: d = -qn / (q - 1)
7. Rearrange: d = nq / -(q - 1)
8. Distribute -1: d = nq / 1 - q