Question #546fd

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.

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)`
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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)`
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Using equation(2)

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

`t=8+32=40`