Can you help me answer this question? I'm confused, and show me how you did it, that way I can understand on how to solve it more?
The total number of students in 8th Grade is 32, including Fran and Billy, Who are one of the female and male students respectively. Fran has twice as many female classmates as the number of male classmates Billy has. How many female students are there in the 8th Grade class?
f+m = 32
f-1 = 2(m-1)
21 females
11 males
check:
Fran has 20 female classmates
Billy has 10 male classmates
Sure! Let's break down the problem step by step.
Step 1: Understand the given information
We are told that the total number of students in the 8th Grade is 32. We also know that Fran and Billy are part of this class, with Fran being female and Billy being male. Additionally, we are given the relationship between the number of female and male classmates they each have.
Step 2: Define the variables
Let's define the number of female classmates Fran has as F and the number of male classmates Billy has as M.
Step 3: Translate the given information into equations
According to the problem, Fran has twice as many female classmates as the number of male classmates Billy has. This can be expressed as:
F = 2M
We also know that the total number of students in the class is 32. Therefore, the sum of female and male classmates must be equal to this total:
F + M = 32
Step 4: Solve the equations
Now we have a system of equations that we can solve simultaneously:
F = 2M and F + M = 32
Substituting the value of F from the first equation into the second equation, we get:
(2M) + M = 32
3M = 32
M = 32/3
M ≈ 10.67
Since we cannot have a fraction of a student, we can round M down to the nearest whole number. Therefore, M = 10.
Step 5: Find the number of female students
Now that we know the number of male classmates, we can substitute M = 10 into the equation F = 2M to find the number of female classmates Fran has:
F = 2(10)
F = 20
Therefore, there are 20 female students in the 8th Grade class.