There are 73 holidays in a year. Find the ratio of the number of working days to the total number of days. In a class of 72 students, 32 students like tennis and the remaining stud... There are 73 holidays in a year. Find the ratio of the number of working days to the total number of days. In a class of 72 students, 32 students like tennis and the remaining students.
Understand the Problem
The question consists of two parts: the first part asks to calculate the ratio of working days to total days in a year given that there are 73 holidays, and the second part provides information about a class of students, where some like tennis. It seems to require calculations related to both parts.
Answer
The ratio is $\frac{292}{365}$; 40 students do not like tennis.
Answer for screen readers
The ratio of working days to total days is $\frac{292}{365}$, and there are 40 students who do not like tennis.
Steps to Solve
- Calculate Total Days in a Year
Typically, a year has 365 days.
- Calculate Working Days
To find the number of working days in a year, subtract the holidays from the total days: $$ \text{Working Days} = \text{Total Days} - \text{Holidays} $$ Substituting the values: $$ \text{Working Days} = 365 - 73 = 292 $$
- Calculate the Ratio of Working Days to Total Days
The ratio of working days to total days can be expressed as: $$ \text{Ratio} = \frac{\text{Working Days}}{\text{Total Days}} = \frac{292}{365} $$
- Simplify the Ratio
To simplify the ratio $\frac{292}{365}$, find the greatest common divisor (GCD). Since 292 and 365 have no common factors other than 1, the ratio cannot be simplified further.
- Determine Remaining Students Who Like Tennis
From a class of 72 students, if 32 students like tennis: $$ \text{Remaining Students} = \text{Total Students} - \text{Students who like Tennis} $$ Substituting the values: $$ \text{Remaining Students} = 72 - 32 = 40 $$
The ratio of working days to total days is $\frac{292}{365}$, and there are 40 students who do not like tennis.
More Information
The ratio of working days to total days, $\frac{292}{365}$, represents the proportion of days in a year that are typically designated as working days. The calculation for students highlights the distribution of interests in a class.
Tips
- Forgetting to subtract holidays when calculating working days.
- Not simplifying the ratio correctly or checking for GCD.
- Miscounting the remaining students.
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