Math Post: How Many Boys and Girls Attended the Dance? (Coursework Sample)

A school dance has 228 students. There are 63 fewer girls than twice as many boys. How many boys and girls attended the dance?
The answer to 131 girls and 97 boys
The initial post should be at least 250 words
Let break down the question as follows
The total number of students = 228
Let the number of boys be, x while that of girls be, y.
This implies that if we sum the x and y we must get the total number of the students in the school dance……
x + y = 228……..let this be our first linear equation,
The second part of the question says that there are 63 fewer girls than twice as many boys are in the school dance. This implies that the number of girls(y) in the school dance is twice the number of boys(x) less 63, given as;
y = 2x -63……………becomes the second linear equation,
x + y= 228……………….1
y = 2x – 63………………2
The system of linear equations can be solved either using substitution method or graphical means.
By substitution,
To get the solution we, substitute for y in the first equation with (2x – 63)
x + (2x - 63) = 228…………then we open the brackets.
x + 2x – 63 = 228……….. Add 2x and x
3x – 63 = 228………..take (-63) to the left side of the equation, it becomes a positive integer.
3x = 228 + 63
3x = 291………………..divide 291 by 3 to get the value of xx = 291/3 = 97
So x = 97, which is the number of boys in the school dance.
To get the number of girls(y) present in the school dance we substitute for x in equation 2
y = 2x – 63
y = 2(97) – 63
= 194 – 63
= 131, which is the number of girls.
Graphical means
To solve the system of linear equations by graphical means, we express the in the form, y = mx + c, where, m and c are constants
And plot their respective graphs, the point of intersection of the two lines gives the values of x and y.
x + y= 228……………….1
y = 2x – 63………………2
Already equation two has the form y = mx + c,
For equation 1 we take x to the LHS of the equation
Y = 228 – x
To plot a g...