SOLUTION: Three boys have marbles in the ratio 19 : 5 : 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the greatest number have? (A) 57 (B) 62

Question 252881: Three boys have marbles in the ratio 19 : 5 : 3. If the boy with the least number has 9 marbles, how many marbles does the boy with the greatest number have?
(A) 57 (B) 62 (C) 48 (D) 54 (E) 70

Found 2 solutions by checkley77, Theo:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
3:9=19:x
3x=9*19
3x=171
x=171/3
x=57 ans. for the greatest number of marbles.
ANSWER A).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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).

RELATED QUESTIONS
Kayla has 120 marbles. If the ratio of red marbles to the total number of marbles is 2 to (answered by oscargut)
Kayla has 120 marbles. If the ratio of red marbles to the total number of marbles is 2 to (answered by oscargut)
Adam, Ben and Calvin had a total of 540 marbles. Adam gave 1/4 of his marbles to Ben.... (answered by josgarithmetic,ikleyn,MathTherapy,greenestamps)
Pam is playing with red and black marbles. the number of red marbles she has is three... (answered by checkley77)
Pam is playing with red and black marbles. The number of red marbles she has is three... (answered by tushki,richwmiller)
If Don Has 2 More Than 3 Times The Number Of Marbles Mark Has,how Many Does Each Boy... (answered by josgarithmetic,Boreal,ikleyn)
A boy has five blue marbles, four green marbles and three red marbles. In how many ways (answered by Edwin McCravy)
Pam is playing with red and black marbles. The number of red marbles she has is three... (answered by checkley77)
Bill and Joe each have a certain number of marbles. If Bill gives Joe five marbles, Bill (answered by lwsshak3)