How can I solve this question with formulas, as opposed to plugging numbers?

You have 3 different coloured marbles - yellow, red and blue.


Number of yellow marbles is 3 x blue, plus 4. The number of red marbles is 5/8 x blue, minus 6.





There are a total of 402 marbles, how many of each marble is there?





Thanks!


J


How can I solve this question with formulas, as opposed to plugging numbers?
Set x equal to blue and write your equation:


Blue = X


yellow = 3X+4


red = 5/8 X - 6


So: X + (3X+4) + (5/8X -6) = 402 and solve for X





The parenthesis aren't necessary except for clarity


since it's all addition or subtraction.


Careful with that fractionHow can I solve this question with formulas, as opposed to plugging numbers?
of yellow marbles = y


# of blue marbles = b


# of red marbles = r





y+b+r=402





y=3b+4


r=5/8b-6





new equation:





(3b+4)+b+(5/8b-6)=402


solve for b





then plug b into the two new formulas. but check the wording of your problem . I think you may have a typo. with the information you gave you should only have 400 marbles
y = # of yellow marbles


b = # of blue


r = # of red





y = 3b + 4


r = (5/8)b - 6


b = (y - 4)/3 ---%26gt; plug into equation for b





---%26gt; r = (5/8) * [(y-4)/3] - 6





also, y + b + r = 402


---%26gt; y + (y - 4)/3 + (5/8) * [(y-4)/3] - 6 = 402





Solve for Y