SOLUTION: A group of boys desiring to group a team to buy a ball. If there had been 3 boys fewer, each would have paid one dollar more; and if there had been 4 boys more, each would have pai

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Question 1182223: A group of boys desiring to group a team to buy a ball. If there had been 3 boys fewer, each would have paid one dollar more; and if there had been 4 boys more, each would have paid 75 cents less. Find the cost of the ball.

->Please help me how to solve this problem step by step.. Thanks in advance!!
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the cost of the ball
Let y be the number of boys

x/y = cost per boy
x/(y-3) = cost per boy if there had been 3 fewer boys
x/(y+4) = cost per boy if there had been 4 more boys

If there had been 3 boys fewer, each would have paid one dollar more...:

x%2F%28y-3%29=%28x%2Fy%29%2B1 [1]

... and if there had been 4 boys more, each would have paid 75 cents less:

x%2F%28y%2B4%29=%28x%2Fy%29-3%2F4 [2]

Solve each equation by multiplying through by the least common denominator.

[1] x%2F%28y-3%29=%28x%2Fy%29%2B1

x%28y%29=x%28y-3%29%2By%28y-3%29
xy=xy-3x%2By%5E2-3y
3x+=+y%5E2-3y [3]

[2] x%2F%28y%2B4%29=%28x%2Fy%29-3%2F4

x%284y%29=x%284%28y%2B4%29%29-3%28y%28y%2B4%29%29
4xy=4xy%2B16x-3y%5E2-12y
16x=3y%5E2%2B12y [4]

Eliminate x between [3] and [4] by multiplying [3] by 16 and [4] by -3 and adding:

48x=16y%5E2-48y
-48x=-9y%5E2-36y
0=7y%5E2-84y
0=7y%28y-12%29

y=0 or y=12. Clearly y=0 makes no sense in the problem, so y=12.

So the number boys is y=12.

Use y=12 in either [1] or [2] to find the cost of the ball.

I leave that much to you....

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let each boy pay x
and number of boys be y
there had been 3 boys fewer, each would have paid one dollar more
(y-3)(x+1) = xy
xy+y-3x -3 =xy
y-3x=3
y=3x+3----------------(1)
(y+4)(x-3/4) = xy
xy -(3/4)y +4x -3 =xy
-3/4 y +4x = 3
multiply by 4
-3y +16x =12--------------(2)
substitute y in (2)
-3(3x+3)+16x =12
-9x-9 +16x =12
7x =21
x= 3
y=3x+3
y= 3*3 +3
y=12
Cost of Ball = 4*12 =48
$48