Question #546fd

2 Answers
Apr 3, 2017

32 Blue marbles and 8 White marbles...

Explanation:

The first equation is #4W+W# 4W stands for blue marbles.

The equation changes to #(4W-18)=(6+W)# when she gaves 18 blue marbles away and receives 6 more White marbles. When you solve the equation it becomes 8 White marbles and 32 blue marbles.

Apr 3, 2017

The initial count of marbles was 40

Explanation:

Let the original count of blue marbles be #b#
Let the original count of white marbles be #w#
Let the total initial count be #t#

Given initial condition #" "b=4w#

It is stated that after a change the counts of blue and white become the same

blue changes by #-18#
white changes by #+6#

So after the change we have:

#b-18=w+6" "....................Equation(1)#

However; the value of blue is such that

#b=4w" "................................Equation(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(2) substitute for b in equation(1) giving the count condition:

#color(magenta)(4w)-18=w+6 #

#color(magenta)("Note that "4w" is actually the count of blue marbles")#

#3w=24#

#color(red)(w=24/3=8)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(2)

#color(red)(b=4xx8=32)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Total initial count of marbles")#

#t=8+32=40#