A class of students had a test. If each boy had got 3 points more for the test, then the average result of the class would had been 1,2 points higher. What percentage of the class are girls?
percentbobs*3+percentgirls*0=1.2
percentboys=.4 or 40 percent
girls then are 60 percent.
Well, if we assume that all the students in the class are either boys or girls (and no other magical creatures), then to find out the percentage of girls in the class, we need more information.
However, I could tell you a joke to lighten the mood while we ponder this problem.
Why did the math book look sad?
Because it had too many problems!
To solve this problem, let's denote the number of boys in the class as B and the number of girls as G. We are given that each boy would have gotten 3 points more, resulting in an average increase of 1.2 points for the entire class.
First, let's summarize the given information:
1. Each boy had gotten 3 points more.
2. The average result of the class would have been 1.2 points higher.
Let's set up the equation to solve for the percentage of girls in the class:
(B * 3) + (G * 0) = (B + G) * 1.2
Since girls did not receive any additional points, we multiply the number of girls (G) by 0.
Now let's simplify the equation:
3B = 1.2(B + G)
Distribute 1.2 to (B + G):
3B = 1.2B + 1.2G
Subtract 1.2B from both sides of the equation to isolate G:
3B - 1.2B = 1.2G
2.8B = 1.2G
Divide both sides of the equation by 2.8 to solve for G:
G = (2.8B) / 1.2
The percentage of girls in the class is given by G / (B + G) * 100:
Percentage of girls = (G / (B + G)) * 100
Substituting the value of G:
Percentage of girls = ((2.8B) / 1.2) / (B + (2.8B) / 1.2) * 100
Simplifying further:
Percentage of girls = ((2.8B) / 1.2) / ((1.2B + 2.8B) / 1.2) * 100
Percentage of girls = ((2.8B) / 1.2) / (4B / 1.2) * 100
Percentage of girls = ((2.8B) / 1.2) * (1.2 / 4B) * 100
Percentage of girls = (2.8 / 4) * 100
Percentage of girls = 70%
Therefore, 70% of the class are girls.
To solve this problem, we need to set up an equation based on the given information. Let's suppose there are 𝑛 students in the class.
Let 𝑥 be the average result of the test for the entire class before any changes.
Let 𝑦 be the percentage of the class that are girls (in decimal form: 𝑦/100).
Then, 𝑛(1−𝑦/100) will be the number of boys in the class.
According to the given information, if each boy had gotten 3 points more, the average result of the class would have been 1.2 points higher. This means that the average result for the entire class would have been (𝑥 + 1.2).
Therefore, we can set up the following equation:
𝑥 = (𝑥 + 1.2) − 3(𝑛(1−𝑦/100))/𝑛
Simplifying the equation, we get:
𝑛𝑥 = 𝑛𝑥 + 1.2𝑛 − 3𝑛 + 3𝑦𝑛/100
Rearranging the terms, we get:
3𝑛𝑦 = 120
Dividing both sides by 3𝑛, we have:
𝑦 = 40/𝑛
From the equation, we can see that the value of 𝑦 (the percentage of girls) depends on 𝑛, the total number of students in the class. Without knowing the value of 𝑛, we cannot determine the exact percentage of girls in the class.