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Answer :
Sure! Let's go through each problem one by one and explain how to solve them:
Problem 7:
- What is being calculated? We need to find out the total amount of money received from selling tickets.
- Info provided: Each ticket costs [tex]\(17 \frac{3}{4}\)[/tex] dollars, and tickets were sold to 45 people.
- Solution steps:
1. Convert [tex]\(17 \frac{3}{4}\)[/tex] to a decimal, which is 17.75 dollars.
2. Multiply 17.75 by 45 to find the total money received.
3. The result is [tex]$798.75$[/tex], which matches option A.
Problem 8:
- What is being calculated? The total hours spent reviewing films.
- Info provided: Each film is [tex]\(2 \frac{1}{4}\)[/tex] hours, and 8 films were reviewed.
- Solution steps:
1. Convert [tex]\(2 \frac{1}{4}\)[/tex] to a decimal, which is 2.25 hours.
2. Multiply 2.25 by 8 to find the total hours spent.
3. The result is 18 hours, matching option E.
Problem 9:
- What is being calculated? The total length of the concert in minutes.
- Info provided: Each song is [tex]\(3 \frac{1}{2}\)[/tex] minutes, and the band played 25 songs.
- Solution steps:
1. Convert [tex]\(3 \frac{1}{2}\)[/tex] to a decimal, which is 3.5 minutes.
2. Multiply 3.5 by 25 to find the concert's total length.
3. The result is 87.5 minutes, which matches option D.
Problem 10:
- What is being calculated? The total miles run in a week.
- Info provided: You run [tex]\(4 \frac{1}{2}\)[/tex] miles every day for 7 days.
- Solution steps:
1. Convert [tex]\(4 \frac{1}{2}\)[/tex] to a decimal, which is 4.5 miles.
2. Multiply 4.5 by 7 to find the total miles run.
3. The result is 31.5 miles, matching option B.
Problem 11:
- What is being calculated? Total earnings for a week of work.
- Info provided: Paid [tex]\(22 \frac{3}{4}\)[/tex] dollars per hour, and worked for 40 hours.
- Solution steps:
1. Convert [tex]\(22 \frac{3}{4}\)[/tex] to a decimal, which is 22.75 dollars.
2. Multiply 22.75 by 40 for total earnings.
3. The result is $910.00, matching option E.
Problem 12:
- What is being calculated? The total time taken to grade essays.
- Info provided: It takes [tex]\(1 \frac{1}{6}\)[/tex] hours per essay, and there are 29 essays.
- Solution steps:
1. Convert [tex]\(1 \frac{1}{6}\)[/tex] to a decimal, which is approximately 1.1667 hours.
2. Multiply 1.1667 by 29 for total grading time.
3. The result is approximately 33.83 hours, matching option A if we convert it to [tex]\(33 \frac{5}{6}\)[/tex].
I hope this detailed explanation helps! Let me know if you have any more questions.
Problem 7:
- What is being calculated? We need to find out the total amount of money received from selling tickets.
- Info provided: Each ticket costs [tex]\(17 \frac{3}{4}\)[/tex] dollars, and tickets were sold to 45 people.
- Solution steps:
1. Convert [tex]\(17 \frac{3}{4}\)[/tex] to a decimal, which is 17.75 dollars.
2. Multiply 17.75 by 45 to find the total money received.
3. The result is [tex]$798.75$[/tex], which matches option A.
Problem 8:
- What is being calculated? The total hours spent reviewing films.
- Info provided: Each film is [tex]\(2 \frac{1}{4}\)[/tex] hours, and 8 films were reviewed.
- Solution steps:
1. Convert [tex]\(2 \frac{1}{4}\)[/tex] to a decimal, which is 2.25 hours.
2. Multiply 2.25 by 8 to find the total hours spent.
3. The result is 18 hours, matching option E.
Problem 9:
- What is being calculated? The total length of the concert in minutes.
- Info provided: Each song is [tex]\(3 \frac{1}{2}\)[/tex] minutes, and the band played 25 songs.
- Solution steps:
1. Convert [tex]\(3 \frac{1}{2}\)[/tex] to a decimal, which is 3.5 minutes.
2. Multiply 3.5 by 25 to find the concert's total length.
3. The result is 87.5 minutes, which matches option D.
Problem 10:
- What is being calculated? The total miles run in a week.
- Info provided: You run [tex]\(4 \frac{1}{2}\)[/tex] miles every day for 7 days.
- Solution steps:
1. Convert [tex]\(4 \frac{1}{2}\)[/tex] to a decimal, which is 4.5 miles.
2. Multiply 4.5 by 7 to find the total miles run.
3. The result is 31.5 miles, matching option B.
Problem 11:
- What is being calculated? Total earnings for a week of work.
- Info provided: Paid [tex]\(22 \frac{3}{4}\)[/tex] dollars per hour, and worked for 40 hours.
- Solution steps:
1. Convert [tex]\(22 \frac{3}{4}\)[/tex] to a decimal, which is 22.75 dollars.
2. Multiply 22.75 by 40 for total earnings.
3. The result is $910.00, matching option E.
Problem 12:
- What is being calculated? The total time taken to grade essays.
- Info provided: It takes [tex]\(1 \frac{1}{6}\)[/tex] hours per essay, and there are 29 essays.
- Solution steps:
1. Convert [tex]\(1 \frac{1}{6}\)[/tex] to a decimal, which is approximately 1.1667 hours.
2. Multiply 1.1667 by 29 for total grading time.
3. The result is approximately 33.83 hours, matching option A if we convert it to [tex]\(33 \frac{5}{6}\)[/tex].
I hope this detailed explanation helps! Let me know if you have any more questions.
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