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(2)/(10) = (4)/(a-3)

Solve the proportion, then leave the fraction in a fraction as simplest form. Thanks! :)

User Leonheess
by
8.2k points

2 Answers

4 votes

Solution:

Step-1: Use cross multiplication


  • (2)/(10) = (4)/(a - 3)

  • 2(a - 3) = 4(10)

Step-2: Simplify both sides


  • 2(a - 3) = 4(10)

  • 2a - 6 = 40

Step-3: Add 6 both sides


  • 2a - 6 + 6 = 40 + 6

  • 2a = 46

Step-4: Divide 2 both sides


  • 2a = 46
  • =>
    (2a)/(2) = (46)/(2)
  • =>
    a = 23

Double-check:

Step-1: Substitute the value of a into the proportion


  • (2)/(10) = (4)/(a - 3)
  • =>
    (2)/(10) = (4)/(23 - 3)
  • =>
    (2)/(10) = (4)/(20)

Step-2: Simplify both sides.


  • (2)/(10) = (4)/(20)
  • =>
    (1)/(5) = (1)/(5) (Correct)

The value of a must be 23 to make the proportion true.

User Gmetal
by
8.6k points
2 votes

Answer:


\displaystyle a = 23

General Formulas and Concepts:

Math

  • Simplifying

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Explanation:

Step 1: Define


\displaystyle (2)/(10) = (4)/(a - 3)

Step 2: Solve for a

  1. [Proportion] Simplify fraction:
    \displaystyle (1)/(5) = (4)/(a - 3)
  2. [Multiplication Property of Equality] Cross-multiply:
    \displaystyle a - 3 = 20
  3. [Addition Property of Equality] Add 3 on both sides:
    \displaystyle a = 23

Here we see that in order for the proportion to be equal, a must equal 23. Plugging in a back into the proportion should yield us a fraction equivalent to the original fraction.

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