Question 252881
let A be the one with the largest number.
let B be the one with the middle number.
let C be the one with the smallest number.


let a = the number of marbles that A has.
let b = the number of marbles that B has.
let c = the number of marbles that C has.


you get:


a:b:c = 19:5:3


C has 9 marbles.


9/3 = 3 which means that C has 3 times the marbles as it's ratio number.


to keep the ratios intact, all others in the chain have to be multiplied by 3.


you get:


a:b:c = 19:5:3 = 57:15:9


this means that A has 57 marbles while B has 15 marbles while C has 9 marbles.


you can also use the ratio formula to find the correct value.


b:c = 5:3


This is the same as b/c = 5/3 since a fraction is a ratio of 2 numbers.


you have b/c = 5/3.
you know that c = 9.
the equation becomes:


b/9 = 5/3
multiply both sides of this equation by 9 to get:
b = (9*5)/3 = 45/3 = 15.


now that you know b, you can solve for a in the same manner.


a:b = 19:5


this is the same as a/b = 19/5.


you have a/b = 19/5.
you know that b is 15.
the equation becomes:


a/15 = 19/5
multiply both sides of this equation by 15 to get:
a = (15*19)/5 = 285/5 = 57


you wind up with:


a = 57
b = 15
c = 9


your question was how many marbles does the boy with the greatest number have?


your answer is selection A (57).