Tricycles and Bicycles

Algebra Level 1

There are a total of 12 bicycles and tricycles at the park. Together they have a total of 29 wheels. How many are bicycles and how many are tricycles?

7 bicycles and 5 tricycles 6 tricycles and 6 bicycles 7 tricycles and 5 bicycles 4 bicycles and 8 tricycles

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s/Julia Ding by s/Julia Ding , 32, USA

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7 solutions

Let the number of bicycles be x then number of tricycles will be 12 - x . Since bicycles have 2 wheels and tricycles 3 , we multiply it to x and 12 - x to obtain the equation 2x + 36 -3x = 29 , thus we would get x = 7 and then 12 - 7 = 5

5 Helpful 0 Interesting 1 Brilliant 0 Confused

You would actually get x=-7, not sure if it is concidental or not that the absolute value was the answer

William Chan - 6 years, 1 month ago

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No, you would have -x=-7, or x=7.

Owen Watson - 6 years, 1 month ago
James Hui
May 14, 2015

Here's a trick solution for you guys! Assume you took down 2 wheels from each bike, so there will be 12*2=24 wheels less, 29-24=5 and these 5 wheels must be from the tricycles. So there is 5 tricycles and 7 bicycles.

3 Helpful 0 Interesting 0 Brilliant 1 Confused
Aaron Warren
May 4, 2015

Let x = # of bicycles

Let y = # of tricycles

x + y = 12

2x + 3y = 29

Multiply to get opposite coefficients for x.

-2(x + y = 12)

-2x + -2y = -24

Add equations to eliminate x, then solve for y.

2x + 3y = 29

+(-2x + -2y = -24)

y = 5

Substitute for y to solve for x.

x + 5 = 12

x = 7

There are 7 bicycles and 5 tricycles.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

No. of Bicycles = x No .of Tricycles = y

x+y = 12 2x+3y = 29

x= 12-y 2x = 29-3y 2x = 24-2y

29- 3y = 24-2y 29-24 = -2y+3y 5 = y x+5 =12 x = 7

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Manan Agarwal
May 20, 2015

since total number of wheels is 29 we try to subtract a number such that the answer when subtracted will give us a multiple of 3..29-11= 18 can be a choice but 11 is not a multiple of 2.Next we subtract 29-14=15 which is 14= 7 bicycles and 15 is 5 tricycles

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Manal Sokaki
May 16, 2015

It's just a question of attempting :) keep trying or get it from first attempt 7x2+5x3=29

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sebastian P
May 9, 2015

is just a simple system of equations
2x+3y=29

x+y=12

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