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Zorluk: OrtaSolving Linear Equations

A fitness tracker records a user's daily steps. On Monday, the user walked a certain number of steps. On Tuesday, they walked 1.51.5 times the number of steps they walked on Monday. On Wednesday, they walked 2,5002,500 fewer steps than they did on Tuesday. If the user walked a total of 21,50021,500 steps over these three days, how many steps did they walk on Monday?

  1. A
    4,750
  2. 6,000Cevap
  3. C
    6,500
  4. D
    8,000
  5. E
    9,000

Cevap

6,000
The correct answer is 6,0006,000. By letting xx represent the steps on Monday, we express Tuesday's steps as 1.5x1.5x and Wednesday's steps as 1.5x−2,5001.5x - 2,500. Summing these expressions gives the equation x+1.5x+1.5x−2,500=21,500x + 1.5x + 1.5x - 2,500 = 21,500. Combining like terms yields 4x−2,500=21,5004x - 2,500 = 21,500. Adding 2,5002,500 to both sides gives 4x=24,0004x = 24,000, and dividing by 44 results in x=6,000x = 6,000.

Adım Adım Çözüm

1
Define the variable and write expressions for each day's steps.
Let xx be the number of steps walked on Monday. Tuesday's steps are 1.5x1.5x, and Wednesday's steps are 1.5x−2,5001.5x - 2,500.
This translates the word problem statements into algebraic terms using a single variable.
2
Set up the linear equation representing the total steps.
x+1.5x+(1.5x−2,500)=21,500x + 1.5x + (1.5x - 2,500) = 21,500
The sum of the steps over the three days must equal the given total of 21,50021,500 steps.
3
Combine like terms and solve for xx.
4x−2,500=21,500⇒4x=24,000⇒x=6,0004x - 2,500 = 21,500 \Rightarrow 4x = 24,000 \Rightarrow x = 6,000
Simplifying the equation isolates the variable to find Monday's step count.

Anahtar Kavram

Formulating and solving a single-variable linear equation from a word problem context.
Tahmini Süre:1m 15s
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Solving Linear Equations

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