4th grade math

Question

This is my daughters 4th grade math home work. My brain is long past this can you help? Mrs. Garcia watches 16 students cycle home after school. She counts 38 wheels. Some of the students are on bicycles, and the rest are on tricycles. How many students are on bicycles

Answer 1

There is an algebraic way of doing this, but not for a 4th grader.  

 

I guess that in 4th grade, guessing and checking would be the way to go.  

 

Each tricycle has 3 wheels and each bicycle has 2 wheels.  

 

So we need two numbers so that the numbers add up to 16 and three times the first plus 2 times the second is 38.  

 

First Number           Second number          Number of wheels

 

  16                             0                                48

  15                             1                                47

  14                             2                                46

 

Do you see the pattern?  Each time we decrease the first number (number of tricycles) by 1, the number of wheels decreases by 1 also.  So decreasing the number of tricycles from 16 to 6 decreases the number of wheels from 48 to 38. 

 

There are 6 tricycles and 10 bicycles.  

Answer 2

Let b = number of bicycles, and t = number of tricylces.

b + t = 16

 

Number of wheels (each bicycle has 2 wheels, each tricycle has 3 wheels)

  2b + 3t = 38.

 

Solve these two equations to get  b = 10, t = 6

 

Answer 3

Ms. Helpless!

 

Using b for bikes, t for tricycles:

 

 

1 b, 12 t

 

4 b, 10 t

 

7 b, 8 t

 

10 b, 6 t    This gives the 16 students.

 

13 b, 4 t

 

16 b, 2 t

 

Frank

Answer 4

First of all, this is a fairly advanced question for 4th grade!

 

I would use trial and error for this problem and this grade level:

 

We know that there are only 16 kids, so we will choose two numbers at random that equal 16.  Let's do 7 and 9.

 

Let's say that 7 are on bicycles and 9 are on tricycles.

 

This would mean that there are 14 wheels + 27 wheels.....[(7*2)+(9*3)].  This equals 41 wheels which is too many.

 

We need to decrease the number of tricycles, so let's try 9 on bicycles and 7 on tricycles.

 

This gives us 18 wheels + 21 wheels = 39 wheels which is still too many.

 

Let's give 10 bicycles and 6 tricycles a try:

 

20 wheels + 18 wheels = 38 wheels.  This is our answer!

 

So in order for her to see 38 wheels, 10 students must have been on bicycles and the other 6 on tricycles.