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Zorluk: ZorBasic Algebraic Expressions and One-Step Equations

An online retailer determines the sale price of a promotional item by reducing the original price, PP dollars, by a discount of DD dollars. The discount is defined as D=16PD = \frac{1}{6} P. If the sale price of the item is 125125 dollars, which of the following equations can be solved to find the original price of the item, in dollars?

  1. A
    16P=125\frac{1}{6} P = 125
  2. B
    P−16=125P - \frac{1}{6} = 125
  3. 56P=125\frac{5}{6} P = 125Cevap
  4. D
    P + \frac{1}{6} P = 125
  5. E
    65P=125\frac{6}{5} P = 125

Cevap

The equation stating that five-sixths of the original price equals one hundred twenty-five is correct.
The correct equation is found by expressing the sale price as the original price minus the discount. The discount is one-sixth of the original price, which is represented by the expression containing five-sixths of the original price. Setting this expression equal to the given sale price of one hundred twenty-five dollars results in the correct equation.

Adım Adım Çözüm

1
Write the relationship for the sale price based on the scenario.
S=P−DS = P - D
The sale price (SS) is the original price (PP) minus the discount amount (DD).
2
Substitute the given expression for the discount (D=16PD = \frac{1}{6} P) into the sale price equation.
S=P−16PS = P - \frac{1}{6} P
This expresses the sale price in terms of the single variable PP representing the original price.
3
Simplify the algebraic expression by combining the like terms.
S=56PS = \frac{5}{6} P
Combining 1P1P and −16P-\frac{1}{6} P gives 56P\frac{5}{6} P because 1−16=561 - \frac{1}{6} = \frac{5}{6}.
4
Substitute the known sale price of 125125 dollars into the simplified equation.
56P=125\frac{5}{6} P = 125
This sets up the final one-step equation needed to find the original price.

Anahtar Kavram

Translating verbal descriptions of discounts into simplified one-step linear equations.
Tahmini Süre:1m 30s
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Konular

Basic Algebraic Expressions and One-Step Equations

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