There are 5 more girls than boys in a class.
If 2 boys join the class, the ratio of girls to boys will be 5:4. Find
(a) the number of girls in the class.
(b) the total number of pupils in the class.
(c) the probability of selecting a boy as the class perfect .
(b+5)/(b+2) = 5/4
b = 10
B. 10+15 = 25
To find the answers to the given questions, let's break down the problem step by step:
Step 1: Assign variables
Let's assign variables to the unknown quantities:
Let G = the number of girls in the class
Let B = the number of boys in the class
Step 2: Set up equations
From the given information, we can deduce the following equations:
Equation 1: G = B + 5 (There are 5 more girls than boys in the class.)
Equation 2: (G + 5) / (B + 2) = 5/4 (If 2 boys join the class, the ratio of girls to boys will be 5:4.)
Step 3: Solve the equations
Solving Equation 1:
Since G = B + 5, we can substitute B + 5 for G in Equation 2.
(B + 5 + 5) / (B + 2) = 5/4
(B + 10) / (B + 2) = 5/4
Cross-multiply:
4(B + 10) = 5(B + 2)
4B + 40 = 5B + 10
Subtract 4B from both sides:
40 = B + 10
Subtract 10 from both sides:
B = 30
Now that we have the value of B, we can substitute it back into Equation 1 to find the value of G.
G = 30 + 5
G = 35
(a) The number of girls in the class is 35.
(b) To find the total number of pupils in the class, we simply add the number of girls and boys.
Total number of pupils = G + B
Total number of pupils = 35 + 30
Total number of pupils = 65
The total number of pupils in the class is 65.
(c) To find the probability of selecting a boy as the class prefect, we need to calculate the probability of selecting a boy from the total number of pupils.
Probability of selecting a boy = Number of boys / Total number of pupils
Probability of selecting a boy = 30 / 65
Hence, the probability of selecting a boy as the class prefect is 30/65.