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
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.
To solve this problem, we need to set up a system of equations based on the given information and then solve them simultaneously.
Let's assume the number of unicycles made is 'x'.
According to the problem, the number of bicycles made is 120 more than the number of unicycles. So, the number of bicycles is (x + 120).
Similarly, the number of tricycles made is 4 times the number of unicycles. Hence, the number of tricycles is 4x.
The problem also states that the number of bicycles is 75 more than the number of tricycles. So, (x + 120) = (4x + 75).
Now, let's solve this equation:
x + 120 = 4x + 75
By subtracting x from both sides, we get:
120 = 3x + 75
By subtracting 75 from both sides, we get:
45 = 3x
Finally, we divide both sides by 3 to solve for x:
45 / 3 = x
So, the number of unicycles made is x = 15.