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§ 5.3A

§ 5.3A. Solving Percent Problems Using Equations. Percent Problems into Equations. To solve a percent problem, we express it as an equation with an unknown quantity. The following table is helpful when translating from a percent problem to an equation. Percent Problems into Equations.

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§ 5.3A

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  1. § 5.3A Solving Percent Problems Using Equations

  2. Percent Problems into Equations To solve a percent problem, we express it as an equation with an unknown quantity. The following table is helpful when translating from a percent problem to an equation.

  3. Percent Problems into Equations Example: Translate into an equation. What is 9% of 65? n = 9%  65 Example: Translate into an equation. 24 is what percent of 144? 24 = n  144

  4. Solving a Percent Problem A percent problem has three different parts. amount = percent  base Any one of the three quantities may be unknown. 1. When we do not know the amount: n = 10%  500 2. When we do not know the base: 50 = 10% n 3. When we do not know the percent: 50 = n 500

  5. n = 9%  65 n = (0.09) (65) n = 5.85 Solving a Percent Problem: Amount Unknown amount = percent  base Example: What is 9% of 65? 5.85 is 9% of 65.

  6. 36 = 6%  n Solving a Percent Problem: Base Unknown amount = percent  base Example: 36 is 6% of what? 36 = 0.06n 36 is 6% of 600.

  7. 24 = n  144 Solving a Percent Problem: Percent Unknown amount = percent base Example: 24 is what percent of 144?

  8. § 5.3B Solving Percent Problems Using Proportions

  9. The Parts of a Percent Proportion Proportions are another way to solve a percent problem. To use this proportion, we need to find the amount, base, and percent number in a word problem.

  10. The Parts of a Percent Proportion 10% of 500 is 50. p is the percent number. The amount, a, is the part compared to the whole. The base, b, is the entire quantity.

  11. The Parts of a Percent Proportion Example: Identify the amount, base, and percent number. What is 9% of 65? The base usually follows the word of. b = 65 The amount, a, is unknown. a = the amount (unknown) The value of p is 9. p = 9 24 is what percent of 144? The base usually follows the word of. b = 144 The amount is 24. a = 24 The value of p is unknown. p = the percent (unknown)

  12. p = 9 a = unknown b = 65 Solving a Percent Problem: Amount Unknown Example: What is 9% of 65? Cross multiply. Divide both sides by 100. Simplify. 5.85 is 9% of 65.

  13. p = 6 a = 36 b = unknown Solving a Percent Problem: Base Unknown Example: 36 is 6% of what? Cross multiply. Divide both sides by 6. Simplify. 36 is 6% of 600.

  14. p = unknown a = 24 b = 144 Solving a Percent Problem: Percent Unknown Example: 24 is what percent of 144? Cross multiply. Divide both sides by 144. Simplify.

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