SOLUTION: divide N102 among three boys A, B and C , so that A gets twice as much as B and C gets 1 1/2 times as much as A. How much does each boy get?

Question 1200974: divide N102 among three boys A, B and C , so that A gets twice as much as B and C gets 1 1/2 times as much as A. How much does each boy get?

Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
A gets twice as much as B.
C gets 1 and 1/2 times as much as A.
let a = the amount that A gets.
let b = the amount that B gets.
let c = the amount that C gets.
your equations are:
a = 2 * b.
c = 3/2 * a.
since a = 2 * b, then c = 3/2 * 2 * b = 3 * b.
you get:
a = 2 * b
b = b
c = 3 * b
a + b + c = 102 becomes 2 * b + b + 3 * b = 102
combine like terms to get 6 * b = 102
solve for b to bet:
b = 102/6 = 17
solve for a to get a = 2 * b = 34
solve for c to get c = 3 * b = 51.
a + b + c = 34 + 17 + 51 = 102, confirming the values for a,b,c are correct.

another way to solve is to translate everything to a, rather than b.
start with:
a = 2b
c = 3/2 * a
from a = 2b, solve for b to get b = a/2.
a is now equal to a.
b is equal to a/2.
c is equal to 3/2 * a.
a + b + c = 102 becomes a + a/2 + 3/2 * a = 102.
combine like terms to get 6a/2 = 102
multiply both sides of this equation by 2 to get:
6a = 204.
solve for a to get:
a = 34.
since b = a/2, then b = 17
since c = 3/2 * a, then c = 51.

you get the same values for a,b,c either way.

your solution is:
A gets N34
B gets N17
C gets N51

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The algebra for solving a problem like this is almost always easier if you take the time to analyze the given information so that you can set up the problem using a single variable.

The number given to B is the smallest, so

let x = number given to B
then 2x = number given to A (twice as many as B)
and 3x = number given to C (1 1/2 times as many as A)

The total is 102:

ANSWERS:
A: 2x = 34
B: x = 17
C: 3x = 51

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

BOYS N A 2b B b C 1.5*2b Total 102

--------simplify and solve for b.

-----------and you can find the other two values.
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