Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did rafael count?

Question

need help

 

Answer 1

Hi Emma -- These types of problems are just a kind of game where you move the numbers and variables around by following simple rules -- like, you do the same thing to both sides of an equation -- or the distributive property -- or most of the time you try to simplify to make it easier on yourself.

 

So,you're given

A. white + yellow = 40

and

B. white = 9 X yellow     //("X" means "times", or multiplication -- and "/" means "divided by", or division)

 

From A, yellow = 40 - white                                  //(subtract white from both sides)

Now you have what yellow is. Plug it into B.

white = 9 X (40 - white) = (9 X 40) - (9 X white)     //(distributive property)

white = 360 - (9 X white)       //(simplifying)

white + (9 X white) = 360      //(add 9 X white to both sides)

white X (1 + 9) = 360           //(distributive property)

white X 10 = 360                  //(simplifying)

white = 360 / 10                  //(divide both sides by 10)

white = 36                           //(simplifying)

yellow = 40 - 36                  //(plug white into A)

yellow = 4                          //(simplifying)

 

Now check the answer -- plug (white = 36) and (yellow = 4) into B:

white = 9 X yellow

36 = 9 X 4 -- it's right!

 

Hope that's helpful.

 

-- Bruce Fletcher

 

 

 

Answer 2

After reading the word (story) problem until you understand it, assign variables.  This problem asks for:

    W=the number of white cars.

    Y = the number of yellow cars   (not needed, since we could just use (40-W))

 

Translate:

  "total of 40 white cars and yellow cars"      means     40 = W + Y

  "9 times as many white cars as yellow cars"   means  9Y = W

 

O.K. the math is easy:

    9W + 9Y = 360        (first equation; multiply (W+Y=40) by 9 to eliminate Y)

    W   - 9Y  = 0           (carefully revise the second equation)

  -------------------   (Elimination method:  add the equations)

    10W      = 360

       W  =  36       Ans:  36 White cars

 

Checking (very important):

    40 = W + Y

    40 = 36 + Y

    4 = Y

  is    9(4) = 36    ?

         36 = 36   ? yes