Before the championship game, Tara and Emek helped organize a stadium section with 800 seats. The scoreboard showed that 37.5% of the section was reserved for visiting supporters and 52.5% for local supporters. Tara converted 37.5% to 0.375 and calculated that the visitors needed 300 seats. Emek found that 52.5% of 800 was 420 seats. Together, the two groups needed 720 seats, leaving 80 seats unassigned. They checked their work another way: the two groups used 90% of the section, so 10% should remain. Since 10% of 800 is 80, their totals agreed. Tara and Emek assigned the remaining seats to tournament staff and confirmed that all 800 seats were accounted for. With the numbers checked, the stadium section was ready for the championship crowd.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4

Hint

Since 37.5% is more than one-third of 800, check whether 30 is a reasonable result.

A student claims that 37.5% of the 800 seats is 30 seats because 0.375 * 800 = 30. Which calculation correctly checks the student's claim?

0.375 * 800 = 300, so the student misplaced the decimal point.0.375 * 800 = 30, so the student is correct.0.0375 * 800 = 300, so the student used the wrong decimal.0.375 + 800 = 800.375, so 37.5% cannot be found by multiplication.

Correct! 37.5% = 0.375, and 0.375 * 800 = 300 seats.

Not quite. Convert 37.5% to 0.375 and multiply carefully by 800.

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Hint

First add the percentages used by the two groups, then subtract that total from 100%.

The visiting supporters use 37.5% of the section and the local supporters use 52.5%. What percent of the 800-seat section remains for tournament staff?

Correct! The supporters use 90% of the section, leaving 10% for staff.

Try again. Add 37.5% and 52.5%, then find how much is left out of 100%.

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Hint

Use the two supporter percentages to determine the percentage that remains out of 100%.

Tara and Emek want to verify that all 800 seats are accounted for. Which method provides a correct independent check using the percentages?

Subtract 37.5% from 52.5% to get 15%, then find 15% of 800.Add 300 and 420 to get 720, then multiply 720 by 10%.Add 37.5% and 52.5% to get 90%, so 10% remains; then find 10% of 800 to get 80 seats.Add 37.5% and 52.5% to get 90%, then find 90% of 80 to check the remaining seats.

Correct! The supporters use 90%, leaving 10%, and 10% of 800 is 80 seats.

Not quite. Find the unused percentage of the entire 800-seat section and use it to check the 80 remaining seats.

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