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Zorluk: KolayAlgebraic Word Problems and Modeling

A catering service charges a fixed base setup fee of $150\$150 plus $25\$25 per guest for a private dinner event. If a client was billed a total of $900\$900 for an event, how many guests attended?

  1. A
    2424
  2. 3030Cevap
  3. C
    3434
  4. D
    3636
  5. E
    4242

Cevap

30 guests attended the event.
The total billing model is represented by the equation 150+25g=900150 + 25g = 900, where gg is the number of guests. Subtracting the fixed setup fee of $150\$150 gives 25g=75025g = 750. Dividing 750750 by 2525 yields g=30g = 30, showing that exactly 3030 guests attended.

Adım Adım Çözüm

1
Formulate a linear modeling equation for total cost
Total Cost=Base Fee+(Rate per Guest×g)\text{Total Cost} = \text{Base Fee} + (\text{Rate per Guest} \times g), where gg represents the number of guests. Thus, 150+25g=900150 + 25g = 900.
The total charge consists of a fixed constant component plus a variable component that depends on the number of guests.
2
Isolate the variable term by subtracting the fixed setup fee from both sides
25g=900−150  ⟹  25g=75025g = 900 - 150 \implies 25g = 750.
Subtracting the fixed fee isolates the portion of the total cost spent strictly on guests.
3
Solve for gg by dividing by the per-guest rate
g=75025=30g = \frac{750}{25} = 30.
Dividing the variable total cost by the rate per guest yields the exact number of attending guests.

Anahtar Kavram

Linear Modeling and Single-Variable Word Problems
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Konular

Algebraic Word Problems and Modeling

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