Question 582661
We can do one variable at a  time, but you need to find three numbers that mean different things (number of bicycles, number of tricycles, and number of tandem bikes), so I would rather use three different letter for those numbers. We could re-use old traditional x, for each part of the problemm, but it could get confusing.
The total number of bikes is the number of front steering handlebars: 144.
How many tricycles?
Tricycles are the only bikes with 3 wheels. All the other bikes have 2.
So if we call the number of tricycles x, the number of other bikes (bicycles and tandem bikes) will be 144-x
The number of wheels will be
{{{3x+2(144-x)=320}}}
Let's find x:
{{{3x+2(144-x)=320}}} --> {{{3x+288-2x=320}}}  (applying distributive property)
{{{3x+288-2x=320}}}  --> {{{(3-2)x+288=320}}} --> {{{x+288=320}}} (collecting like terms, which is also the distributive property)
{{{x+288=320}}} --> {{{x+288-288=320-288}}} --> {{{highlight(x=32)}}}
How many tandem bikes?
Tandem bikes have 4 pedals, while all the other bikes have just 2.
Do you want to call the number of tandem bikes y? We could call it x, if we remember that we are recycling and this x is not the same x as before, but I'd rather use a different letter.
If the number of tandem bikes is y, the number of other bikes (bicycles and tricycles) is 144-y.
The total number of pedals is
{{{4y+2(144-y)=378}}}
Let's find y:
{{{4y+2(144-y)=378}}} --> {{{4y+288-2y=378}}} --> {{{(4-2)y+288=378}}} --> {{{2y+288=378}}} --> {{{2y+288-288=378-288}}} --> {{{2y=90}}} --> {{{2y/2=90/2}}} --> {{{highlight(y=45)}}}
So we know there are 32 tricycles and 45 tandem bikes.
How many bicycles.
If z is the number of bicycles, the total number of bikes is
{{{z+32+45=144}}} --> {{{z+77=144}}} --> {{{z+77-77=144-77}}} --> {{{highlight(z=67)}}}