The number of boys in a class is 10 less than twice the number of girls.
Find the total number of the students in the class, if the number of boys is 5 more than the number of girls.
let's start with "the number of boys is 5 more than the number of girls"
---> b = g+5
and "the number of boys in a class is 10 less than twice the number of girls"
---> b = 2g - 10
so 2g - 10 = g + 5
continue
Ana = Saba (around 5:15 am)
Let's solve this using a step-by-step approach.
Step 1: Let's assign variables to the number of boys and girls in the class.
Let B be the number of boys.
Let G be the number of girls.
Step 2: Translate the given information into equations.
We are given two pieces of information:
1) The number of boys is 10 less than twice the number of girls. This can be written as:
B = 2G - 10.
2) The number of boys is 5 more than the number of girls. This can be written as:
B = G + 5.
Step 3: Set the two equations equal to each other.
From step 2, we have:
2G - 10 = G + 5.
Step 4: Solve the equation for G.
Combine like terms:
2G - G = 5 + 10,
G = 15.
Step 5: Find the value of B using one of the given equations.
Substitute G = 15 into B = G + 5:
B = 15 + 5,
B = 20.
Step 6: Find the total number of students in the class.
The total number of students is the sum of the number of boys and girls:
Total = B + G,
Total = 20 + 15,
Total = 35.
So, the total number of students in the class is 35.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of girls in the class is 'g' and the number of boys is 'b'.
According to the first statement, "The number of boys in a class is 10 less than twice the number of girls", we can form the equation:
b = 2g - 10
According to the second statement, "The number of boys is 5 more than the number of girls", we can form the equation:
b = g + 5
Now we have a system of equations:
b = 2g - 10 (equation 1)
b = g + 5 (equation 2)
Since both equations express b in terms of g, we can set them equal to each other to solve for g:
2g - 10 = g + 5
Simplifying the equation, we get:
2g - g = 5 + 10
g = 15
Now substitute the value of g back into either of the original equations to solve for b:
b = g + 5
b = 15 + 5
b = 20
Therefore, there are 15 girls and 20 boys in the class. To find the total number of students, we add the number of girls and boys together:
Total number of students = number of girls + number of boys
Total number of students = 15 + 20
Total number of students = 35
So, there are 35 students in the class.