SOLUTION: A cycle shop sells bicycles and tricycles. The number of bicycles is 1 less than 4 times the numberm of tricycles. All the bicycles and tricycles together have 174 wheels. How many

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A cycle shop sells bicycles and tricycles. The number of bicycles is 1 less than 4 times the numberm of tricycles. All the bicycles and tricycles together have 174 wheels. How many      Log On

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Question 451781: A cycle shop sells bicycles and tricycles. The number of bicycles is 1 less than 4 times the numberm of tricycles. All the bicycles and tricycles together have 174 wheels. How many bicycles are there?
Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
If we mark number of bicycles as b and number of tricycles as t then we have the following:
b is by 1 less than 4 times t -> b=4t-1

Knowing that bicycle has 2 wheels and tricycle has 3 we have:
total number of wheels is 174 -> 2b%2B3t=174

Substitute b in the second equation with the first:

2%284t-1%29%2B3t=174 , multiply
8t-2%2B3t+++=174 , combine
11t-2+++++=174 , add 2 to the both sides of equation
11t+++++++=176 , divide both sides by 11
++t+++++++=16 , this is the number of tricycles

b=4t-1 , substitute t with 16
b=4%2A16-1=63 , this is the number of bicycles

check:
2b+3t=2*63+3*16=126+48=174, OK