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Zorluk: OrtaFractions, Decimals, and Percentages

At a community theater, ticket sales for a weekend musical were divided among three ticket categories: advance online purchases, box office walk-ups, and discounted student passes. Advance online purchases accounted for 25\frac{2}{5} of total ticket sales, and box office walk-up sales accounted for 35%35\% of total ticket sales. If the remaining 125 tickets sold were discounted student passes, what was the total number of tickets sold for the musical?

  1. A
    375
  2. 500Cevap
  3. C
    167
  4. D
    313
  5. E
    94

Cevap

The total number of tickets sold for the musical was 500.
Advance online tickets represent 25=40%\frac{2}{5} = 40\% of the total. Adding the 35%35\% from box office walk-ups gives 75%75\% of total sales accounted for. The remaining 25%25\% of sales corresponds to the 125 student passes. Setting 25%25\% of the total equal to 125 and solving gives a total of 500 tickets.

Adım Adım Çözüm

1
Convert the fraction of advance online tickets to a percentage.
25=40100=40%\frac{2}{5} = \frac{40}{100} = 40\%
Converting all proportions to percentages allows for direct comparison and addition.
2
Calculate the combined percentage of advance online and box office ticket sales.
40%+35%=75%40\% + 35\% = 75\%
Adding the two known categories determines the total portion of non-student ticket sales.
3
Find the percentage corresponding to the discounted student passes.
100%−75%=25%100\% - 75\% = 25\%
The sum of all categories must equal 100%100\% of total sales.
4
Set up an equation relating the remaining percentage to the total ticket count TT.
0.25×T=125  ⟹  T=1250.25=5000.25 \times T = 125 \implies T = \frac{125}{0.25} = 500
Dividing the part by its corresponding percentage rate yields the whole amount.

Anahtar Kavram

Solving multi-step word problems involving conversions between fractions, percentages, and whole numbers.
Tahmini Süre:1m 30s
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Fractions, Decimals, and Percentages

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