In Mrs. Harrington’s history class, 80% of the students speak English and 60% speak German. There are 30 students who can speak only one language. What is the maximum number of students who may speak both English and German in her class?
so I think i'm supposed to start with finding the total, but i don't know where to begin. can you please show all your steps and why.
Sure! Let's break down the problem step by step.
Step 1: Find the total number of students in Mrs. Harrington’s history class.
To find the total number of students, we can use the concept of percentages. We are given that 80% of the students speak English and 60% speak German. Since the percentages are not overlapping, that means all the students fall into one of these categories (English only, German only, or both English and German). Therefore, the total percentage of students in the class is 100%.
Step 2: Calculate the percentage of students who can speak only one language.
From the problem, we are told that there are 30 students who can speak only one language. Since we don't know the total number of students in the class, we need to find the percentage of students represented by these 30 students who can speak only one language.
Let's say the total number of students in the class is "N".
The percentage of students who can speak only one language is given by (30/N) * 100.
Step 3: Calculate the percentage of students who can speak both English and German.
Since the maximum number of students who may speak both English and German is asked, we want to find the maximum amount of overlap between the English-speaking students and the German-speaking students. Therefore, the percentage of students who can speak both languages is the difference between the percentages of students who speak English only and German only.
Let's denote:
- "E" as the percentage of students who speak English only,
- "G" as the percentage of students who speak German only,
- "B" as the percentage of students who speak both English and German.
The equation is: E - B = G
Step 4: Calculate the maximum number of students who may speak both English and German.
Now, we can substitute the values we have so far into the equation to solve for the maximum number of students who may speak both English and German.
Let's say E is 80%. Since G is 60% and B is what we are trying to find, we get:
80% - B = 60%
Simplifying the equation:
80 - B = 60
B = 80 - 60
B = 20%
Finally, to find the maximum number of students who may speak both English and German, we need to calculate 20% of the total number of students.
Step 5: Calculate the maximum number of students who may speak both languages.
To get the maximum number of students who may speak both English and German, we multiply the percentage B (20%) by the total number of students.
Let's denote "X" as the maximum number of students who may speak both languages.
The equation is: (20/100) * N = X
By solving this equation, we can find the maximum number of students who may speak both English and German in Mrs. Harrington's history class.
Note: Without the total number of students in the class (N), we cannot find actual numerical values for the number of students. However, using the steps provided, you can calculate the maximum number based on any given total number of students.
Oh, history class, where all the ancient secrets of the world are revealed, like the fact that 80% of the students speak English and 60% speak German. It's a linguistic bonanza! So, let's embark on this language-filled adventure together.
First, let's find out the maximum number of students who may speak both English and German in Mrs. Harrington's class. To do that, we need to focus on those who can only speak one language. And it just so happens that we have been blessed with the divine knowledge that there are 30 students who fit this description.
Now, let's break it down. If 80% of the students can speak English, that means only 20% (100% - 80%) of them cannot. Similarly, 40% (100% - 60%) of the students cannot speak German since 60% of them do.
Now, here comes the moment of truth. To find the maximum number of students who may speak both English and German, we need to add the number of students who can only speak English to the number of students who can only speak German.
If 20% of the students cannot speak English, then the number of students who can only speak English is 30 students multiplied by 20% (or 0.2): 30 x 0.2 = 6 students.
Similarly, if 40% of the students cannot speak German, then the number of students who can only speak German is 30 students multiplied by 40% (or 0.4): 30 x 0.4 = 12 students.
Now, let's combine the number of students who can only speak English (6) with the number who can only speak German (12): 6 + 12 = 18 students.
Voila! The maximum number of students who may speak both English and German in Mrs. Harrington's class is 18. I hope that answers your question and brightens up your day with some linguistic antics!
Sure! Let's break down the problem step by step.
Step 1: Find the total number of students who speak either English or German.
Since 80% of the students speak English and 60% speak German, we can calculate the total number of students who speak either language by adding these two percentages: 80% + 60% = 140%.
Step 2: Calculate the number of students who can only speak one language.
The problem states that there are 30 students who can speak only one language.
Step 3: Find the number of students who can speak both English and German.
To find the maximum number of students who may speak both English and German, we need to subtract the number of students who can speak only one language from the total number of students who speak either English or German.
So, 140% - 30 = 110%.
Therefore, the maximum number of students who may speak both English and German in Mrs. Harrington's class is 110.
I doubt there any students who speak no language, so since (80+60) = 140%, 40% speak both English and German.
So, 40% speak only English and 20% speak only German.
That means that 60% of the students speak only one language.
So, if there are x students,
.60x = 30
x = 50
40% of 50 is 40 who speak both.