Question

Translate the given statement into a linear equation in the form

ax + by = c
using the indicated variable names. Do not try to solve the resulting equation.
There are twice as many soccer fans (x) as football fans (y).

Answer 1

x - 2y = 0

Explanation:

So the starting point here is the sentence:

"There are twice as many soccer fans (x) as football fans (y)."

There are MORE soccer fans than football fans.

So x is the soccer fans and y is the football fans.

Let's just put them in the same math sentence together:

x = y

well, obviously this is wrong but the word "twice" means we are going to times something times 2, but which variable? Since the x is a bigger number ("twice as many soccer fans... ") x and y are not equal...and to make them equal, we have to double the football fans.

Here is what the sentence says:

x = 2y

Now in the problem, they asked for the format

ax + by = c

That means the y term needs to be moved over to the left side of the equation.

x = 2y

subtract 2y from both sides.

x - 2y = 0

this is in the format

ax + by = c

The equation is

x - 2y = 0