What is your Grade? (Problem 1)

$\frac{x_1 + x_2 + x_3}{3}$ $= x_1 - 7$ $(1)$

$x_1 = x_2$ $(2)$

$x_3 + y = x_1 = x_2$ $(3)$

These are your trimultaneous equations (three simultaneous equations).

Since equations $2$ and $3$ are similar, you can eliminate equation $2$ . What's left is a pair of simultaneous equations:

$\frac{x_1 + x_2 + x_3}{3}$ $= x_1 - 7$ $(1)$

$x_3 + y = x_1 = x_2$ $(2)$

Now substitute equation $2$ into equation $1$ and simplify. You should get:

$\frac{3x_3 + 2y}{3}$ $= x_1 - 7$ $(1)$

Now, multiply both sides by $3$ and simplify:

$3x_3 + 2y = 3x_1 - 21$

Now, since you know that $x_1 = x_3 + y$ , substitute this into $3x_3 + 2y = 3x_1 - 21$ and simplify (you may want to use $3x_3 + 2y = 3(x_1 - 7)$ to help):

$2y = 3y - 21$

$0 = 3y - 2y - 21 = y - 21$

$21 = y$

Now substitute $21 = y$ into equation $1$ and simplify:

$\frac{3x_3 + 42}{3}$ $= x_1 - 7$ $(1)$

Now, think. You know that in GCSE Mathematics papers, the maximum you can get is $80$ .

So, using $x_3 + 21 = x_1 = x_2$ , which is equation $2$ :

$x_3 = x_1 - 21 = x_2 - 21$

$80 - 21 = 59 = x_3$

Now, substitute $59 = x_3$ into equation $1$ :

$\frac{3(59) + 42}{3}$ $= x_1 - 7$ $(1)$

$\frac{219}{3}$ $= x_1 - 7$ $(1)$

$73 = x_1 - 7$ $(1)$

Now, substitute $x_1 = 80$ into equation $1$ :

$73 = 80 - 7$

$73 \equiv 73$

Therefore, your total grade is $73$ .