Question 161501: Pop's Cycle Shop sells bicycles and tricycles. The number of bicycles is 1 less than 5 times the number of tricycles. All the bicycles and tricycles together have a total of 154 wheels. How many bicycles are there?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let b = number of bicycles
let t = number of tricycles
number of bicycles is 5 times the number of tricycles minus 1 becomes
b = 5*t - 1
subtract b from both sides of the equation and add 1 to both sides of the equation and it becomes
1 = 5*t - b
which is the same as
5*t - b = 1
since a bicycle has 2 wheels and a tricycle has 3 wheels, 2 times the number of bicycles plus 3 times the number of tricycles totals the number of wheels which is 154, so the equation becomes
2*b + 3*t = 154 which is the same as 3*t + 2*b = 154
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2 equations to solve simultaneously are:
5*t - b = 1
3*t + 2*b = 154
multiply both sides of the first equation by 2 to change the first equation to
10*t - 2*b = 2 which will allow us to cancel out the b's.
simultaneous equations are now
10*t - 2*b = 2
3*t + 2*b = 154
add first equation to second equation to get
13*t + 0*b = 156
which becomes
13*t = 156
which becomes
t = 156 / 13 = 12
so,
t = 12
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original equations copied here for ease of reference:
2 equations to solve simultaneously are:
5*t - b = 1
3*t + 2*b = 154
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substitute 12 for t in the first equation to get
5*12 - b = 1
which becomes
60 - b = 1
adding b to both sides of the equation and subtracting 1 from both sides of the equation gets
60 - 1 = b
which becomes
b = 59
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substituting 59 for b and 12 for t in the second equation and it becomes
3*12 + 2*59 = 154
which becomes
36 + 118 = 154
which becomes
154 = 154 proving the answer is correct.
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answer is:
12 tricycles and 59 bicycles
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