Question

Some bikes and trikes are on the playground. there are 7 seats and 19 wheels. how many bikes are there? how many trikes are there?

Answer 1

Let x the number of bikes, and y the number of trikes.
We have the equations:
x+y=7 (only one seat )
2x+3y=19 (two wheels for a bikes and three wheels for each trike)
Solving the above system for x and y we get:
x=2, y=5.
So there are two bikes and 5 wheels.
For solving, use x = 7-y, then using the second equation
2(7-y)+3y=19. solving the above equation for y we get y=5 then
deduce x=7-y=7-5=2.

Answer 2

Answers:

There are 2 bikes there

There are 5 trikes there

Step-by-step explanation

Let the number of bikes be represented by b

Let the number of trikes be represented by t

Given,

There are a total of 7 seats

We know that each bike and each trike has only a seat,

Therefore, b + t = 7 … (Equation I)

Given,

There are a total of 19 wheels.

We know that each bike has 2 wheels

And each trike has 3 wheels

Therefore, 2b + 3t = 19 … (Equation II)

b + t = 7 … (Equation I)

b = 7 – t … (Equation III)

Substitute 7 – t for b in equation II

2b + 3t = 19 … (Equation II)

2(7 – t) + 3t = 19

14 – 2t + 3t = 19

14 + t = 19

Subtract 14 from both sides of the equation

14 + t = 19

14 – 14 + t = 19 – 14

t = 5

Therefore, there are 5 trikes

To find the value of b, substitute 5 for t in Equation III

b = 7 – t … (Equation III)

b = 7 – 5

b = 2

Therefore, there are 2 bikes