Fractions, Decimals, and Percentages

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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 $\frac{2}{5}$ of total ticket sales, and box office walk-up sales accounted for $35\%$ 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?

375

500

167

313

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Cevap: 500

Cevap

The total number of tickets sold for the musical was 500.

Advance online tickets represent

\frac{2}{5} = 40\%

of the total. Adding the

35\%

from box office walk-ups gives

75\%

of total sales accounted for. The remaining

25\%

of sales corresponds to the 125 student passes. Setting

25\%

of the total equal to 125 and solving gives a total of 500 tickets.

Adım Adım Çözüm

Convert the fraction of advance online tickets to a percentage.

\frac{2}{5} = \frac{40}{100} = 40\%

Converting all proportions to percentages allows for direct comparison and addition.

Calculate the combined percentage of advance online and box office ticket sales.

40\% + 35\% = 75\%

Adding the two known categories determines the total portion of non-student ticket sales.

Find the percentage corresponding to the discounted student passes.

100\% - 75\% = 25\%

The sum of all categories must equal

100\%

of total sales.

Set up an equation relating the remaining percentage to the total ticket count

T

0.25 \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.

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Fractions, Decimals, and Percentages

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