There are 27 students in Mrs. Reeds class. The number of boys and number of girls are both composite numbers. There are 3 more girls than boys. How many girls and how many boys are in the class?
Let's solve this step-by-step.
Step 1: Since the number of boys and girls are both composite numbers, we need to find two composite numbers that have a difference of 3.
Step 2: The prime numbers less than 27 are 2, 3, 5, 7, 11, 13, 17, 19, 23. We know that the composite numbers are multiples of prime numbers.
Step 3: Based on this, we can try combinations of composite numbers that meet the given conditions.
Let's start with the prime numbers 2 and 5:
- If there are 5 boys and 8 girls, the total number of students would be 13, which is less than 27.
- If there are 10 boys and 13 girls, the total number of students would be 23, which is still less than 27.
Let's try the prime numbers 2 and 7:
- If there are 7 boys and 10 girls, the total number of students would be 17, which is still less than 27.
Let's try the prime numbers 3 and 5:
- If there are 5 boys and 8 girls, the total number of students would be 13, which is still less than 27.
Let's try the prime numbers 3 and 7:
- If there are 7 boys and 10 girls, the total number of students would be 17, which is still less than 27.
After trying different combinations, we see that none of them result in a total of 27 students.
Therefore, it seems that there might be a mistake or missing information in the provided problem statement.
To determine the number of girls and boys in Mrs. Reed's class, let's break down the given information step by step.
1. "There are 27 students in Mrs. Reed's class." This provides us with the total number of students in the class.
2. "The number of boys and number of girls are both composite numbers." Composite numbers are positive integers greater than 1 that can be divided evenly by numbers other than 1 and itself. We need to find pairs of composite numbers whose sum equals 27.
3. "There are 3 more girls than boys." Let's denote the number of boys as "b" and the number of girls as "g." According to the given information, g = b + 3.
Now, let's find pairs of composite numbers whose sum equals 27. We can start by listing the possible composite numbers less than 27: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, and 25.
We need to find a pair of numbers whose sum equals 27. We can try different combinations until we find the one that satisfies the condition g = b + 3.
Let's go through the list of composite numbers and check each pair:
- 4 + 23 = 27 (fail, no integer solution for g and b)
- 6 + 21 = 27 (fail, no integer solution for g and b)
- 8 + 19 = 27 (fail, no integer solution for g and b)
- 9 + 18 = 27 (fail, no integer solution for g and b)
- 10 + 17 = 27 (fail, no integer solution for g and b)
- 12 + 15 = 27 (success, b = 12 and g = 15)
Therefore, there are 15 girls and 12 boys in Mrs. Reed's class.
X Boys
(X+3) Girls.
x + (x+3) = 27.
2x = 27-3 = 24
X = 12.
X+3 = 15.