The average mass of a group of girls is 45 kg. After Sally who weighs 63 kg joins the group, the average mass becomes 48 kg. How many girls are there in the group including Sally?
Question
The average mass of a group of girls is 45 kg. After Sally who weighs 63 kg joins the group, the average mass becomes 48 kg. How many girls are there in the group including Sally?
Solution
Let's solve this step by step:
Step 1: Let's denote the number of girls in the group before Sally joined as 'x'.
Step 2: The total mass of the group before Sally joined is the average mass times the number of girls, which is 45x.
Step 3: After Sally joined, the number of girls became 'x+1' and the average mass became 48 kg. So, the total mass of the group after Sally joined is 48(x+1).
Step 4: The total mass of the group after Sally joined is also equal to the total mass before she joined plus her mass. So, we can set up the equation 45x + 63 = 48(x+1).
Step 5: Solve the equation. First, distribute 48 to 'x' and '1' to get 45x + 63 = 48x + 48.
Step 6: Subtract 45x from both sides to get 63 = 3x + 48.
Step 7: Subtract 48 from both sides to get 3x = 15.
Step 8: Divide both sides by 3 to solve for 'x'. x = 5.
Step 9: Remember 'x' is the number of girls before Sally joined. So, the number of girls in the group including Sally is x + 1 = 5 + 1 = 6.
So, there are 6 girls in the group including Sally.
Similar Questions
The average weight of a group of 50 girls was calculated as 58 kg. It was later discovered that the weight of one of the girls was read as 45 kg, whereas her actual weight was 65 kg. What is the actual average weight of the group of the 50 girls?
In a primary school the average weight of male students is 65.9 kgs and the average weight of female students is 57 kg.If the average weight of all the students is 60.3kg and the number of male students in the school is 66.What is the number of female students in the school?11411266None of these
There are 40 students in a class whose average weight is 56. 25kg.Among these 40 students 25 are boys and 15 are girls. The average weight of 25 boys is 6.8 kg more than the average weight of 15 girls. What is the average weight of 15 girls?
The ratio of the number of boys and girls in a class is 5 : 3. If the average weight of all the boys is 63 kg, whereas that of the girls is 47 kg, find the average weight (in kg) of all the students in the class.
The average weight of a certain number of students in a group is 72 kg. If 10 students having an average weight of 78 kg leave and 4 students having an average weight of 80 kg join the group, the average weight of the students in the decreases by 0.7 kg. The number of students initially in the group is?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.