Question

The local pre-school ordered all new bicycles and tricycles for the new school year. Each bicycle and tricycle is shipped in its own box. Oddly, the manufacturer shipped all of the wheels in a separate box. If there are 16 boxes of bicycles/tricycles total and 45 wheels total, how many tricycles were ordered?
please don't just put an answer i need an explanation too

Answer 1

There are 16 boxes total, and 45 wheels total. 

we know that each bicycle/tricycle is in it's own box. 
i'm going to use the variable "b" for bicycle and "t" for tricycle

b + t = 16 
(because b is the amount of bicycles and t is the amount of tricycles) 

now we know that there are 45 wheels total. 
there are 2 wheels for a bicycle and 3 wheels for a tricycle

2b + 3t = 45 

now we have a system of equations
b + t = 16
2b + 3t = 45 

You can solve this multiple ways, but I'm going to use substitution. 
b + t = 16 can also be written as b = 16 - t (if you subtract both sides by t) 
then we can substitute this b = 16 - t into the other equations

2(16 - t) + 3t = 45

32 - 2t + 3t = 45
32 + t = 45
t = 13 

now you can plug that back into the original equations

b + 13 = 16 
b = 3

2b + 3(13) = 45
2b + 39 = 45
2b = 6
b = 3

If you have any more questions, feel free to ask!