Question

a cycle company make bicycles, tricycles an unicycles. Last week they made 120 more bicycles than unicycles, and 4 times as many tricycles as unicycles. If they made 75 more bicycles than tricycles, how many unicyles did they make?

I don't understand how to do this, please help

Answer 1

just put the words into symbols. If there are
u unicycles,
b bicycles, and
t tricycles,

b = u+120
t = 4u
b = t+75

Now you can just start substituting and watch the variables get resolved:

t=4u, so

b = u+120
b = 4u+75
so
u+120 = 4u+75
3u = 45
u=15
so, b=u+120=135
t=4u = 60

So, they made
15 unicycles
135 bicycles
60 tricycles

check that the numbers satisfy the original conditions. They do.