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christopher is walking past a bike shop and looks inside. He sees some bicycles and some tricycles. He sees 32 seats and 77 wheels. How many tricycles are in the shop.

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GoddessofDork
  • Bicycles: 1 seat and 2 wheels
  • Tricycles: 1 seat and 3 wheels

So with this, we will be making a system of equations. One representing the amount of seats and one representing the amount of wheels. Let x = bicycles and y = tricycles:

[tex] x+y=32\\2x+3y=77 [/tex]

With this, I will be using the substitution method. Firstly, subtract y on both sides of the first equation:

[tex] x=32-y\\2x+3y=77 [/tex]

Next, substitute x in the second equation for (32 - y) and solve for y:

[tex] 2(32-y)+3y=77\\64-2y+3y=77\\64+y=77\\y=13 [/tex]

In short, there are 13 tricycles.

tramserran

A bicycle has 2 wheels and a tricycle has 3 wheels. Both have only 1 seat so he saw a total of 32 bikes.

Let "x" represent the number of bicycles and "y" represent the number of tricycles. The solution below is using the substitution method.

x + y = 32 → x = 32 - y

2x + 3y = 77 → 2(32 - y) + 3y = 77 → 64 - 2y + 3y = 77 → 64 + y = 77 → y = 13

Answer: 13 tricycles

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