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Zorluk: OrtaBasic Algebraic Expressions and One-Step Equations

A specialty coffee roasting facility packages a batch of cc pounds of dark roast coffee beans into retail bags. Each bag is filled with exactly 1.51.5 pounds of coffee. If the facility completely fills 2828 bags with no coffee left over, which of the following equations can be used to find the total weight, cc, in pounds, of the coffee batch?

  1. c1.5=28\frac{c}{1.5} = 28Cevap
  2. B
    1.5c=281.5c = 28
  3. C
    c−1.5=28c - 1.5 = 28
  4. D
    1.5c=28\frac{1.5}{c} = 28
  5. E
    c+1.5=28c + 1.5 = 28

Cevap

The equation that can be used to find the total weight is c1.5=28\frac{c}{1.5} = 28.
To find the number of bags filled, the total weight of coffee (cc) must be divided into equal parts of 1.51.5 pounds each. Setting this quotient equal to the total number of filled bags (2828) gives the equation c1.5=28\frac{c}{1.5} = 28.

Adım Adım Çözüm

1
Identify the given quantities and unknown variable
Total weight = cc pounds; Weight per bag = 1.51.5 pounds; Total number of bags = 2828.
Establishing clear variable definitions is necessary before setting up an algebraic model.
2
Formulate the relationship between total quantity, unit rate, and total items
Total WeightWeight per Bag=Total Number of Bags\frac{\text{Total Weight}}{\text{Weight per Bag}} = \text{Total Number of Bags}
Dividing a total quantity by the capacity of one container gives the total number of containers filled.
3
Substitute the known values and variable into the relationship formula
c1.5=28\frac{c}{1.5} = 28
This yields the correct one-step linear equation representing the scenario.

Anahtar Kavram

Writing one-step linear equations from word problems involving rates and equal grouping
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Basic Algebraic Expressions and One-Step Equations

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