The number of boys in a certain class exceed the number of girls by 7. If the number of boys is 5/4 of the number of girls, how many boys are there in the class?
The choices of answers are:
a) 21
b) 28
c) 35
d) 42
e) 63
I figured out that the answer is 35, but I did it by subtracting each of the possible answers by 7 and then multiplying that answer by 5/4.
This is what I did to get my final answer using 35: 35 - 7 = 28; 5/4 X 28/1 = 140/4 which equals 35.
Now, I know there must be a simplier way to get that answer.
Can you show me step by step? Thanks.
B-7=G
B= 5/4 * G = 5G/4
5G/4-7=G
5G-28=4G
G=28
B=28+7=35
G=28
Thanks very much.
Absolutely! Let's figure this out together, step by step!
1. Let's represent the number of girls as 'g'.
2. According to the problem, the number of boys exceeds the number of girls by 7. So, we can represent the number of boys as 'g + 7'.
3. It is also given that the number of boys is 5/4 of the number of girls. This can be written as an equation: 'g + 7 = (5/4)*g'.
4. To simplify the equation, let's first get rid of the fraction by multiplying both sides by 4: '4 * (g + 7) = 5 * g'.
5. Expanding the equation, we get: '4g + 28 = 5g'.
6. Now, let's isolate 'g' by subtracting '4g' from both sides: '4g - 4g + 28 = 5g - 4g'.
This simplifies to '28 = g'.
7. Therefore, the number of girls in the class is 28.
Now that we know the number of girls, we can find the number of boys by substituting 'g' into 'g + 7':
28 + 7 = 35.
So, there are 35 boys in the class. The correct answer is option (c) 35. Well done for figuring it out!
Let's solve this step-by-step:
Let's assume the number of girls in the class as "x".
According to the problem, the number of boys exceeds the number of girls by 7.
Therefore, the number of boys = x + 7.
It is given that the number of boys is 5/4 of the number of girls.
Therefore, (x + 7) = (5/4) * x.
To solve this equation, we can start by multiplying both sides of the equation by 4 to eliminate the fraction:
4 * (x + 7) = 5 * x.
4x + 28 = 5x.
Now, we can subtract 4x from both sides of the equation:
4x - 4x + 28 = 5x - 4x.
28 = x.
Therefore, the number of girls, x = 28.
To find the number of boys, substitute the value of x in the equation (x + 7):
Number of boys = 28 + 7 = 35.
So, there are 35 boys in the class.
Therefore, the correct answer is c) 35.
Sure! To find the number of boys in the class, we can use a system of equations and solve for the unknown variables. Let's represent the number of girls as G and the number of boys as B.
From the given information, we have two equations:
1) B = G + 7 (The number of boys exceeds the number of girls by 7)
2) B = (5/4)G (The number of boys is 5/4 of the number of girls)
To solve the system of equations, we can substitute equation 1) into equation 2):
G + 7 = (5/4)G
First, let's multiply both sides of the equation by 4 to get rid of the fraction:
4*(G + 7) = 5G
Distribute 4 to both terms inside the parentheses:
4G + 28 = 5G
Now, subtract 4G from both sides of the equation:
28 = 5G - 4G
Combine like terms:
28 = G
So the number of girls in the class is 28. To find the number of boys, we can substitute this value back into equation 1):
B = G + 7
B = 28 + 7
B = 35
Therefore, the number of boys in the class is 35.
The correct answer is c) 35.