Question 1153556: Several friends decided to equally share the $525 cost of the set of cookware for a wedding gift. However, before the wedding, 6 more friends joined the others in giving the couple the cookwares. This lowered the contribution of each person by $10. How many friends originally agreed to share of the cost of the cookware?
Found 3 solutions by math_helper, Theo, VFBundy:
Answer by math_helper(2461)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! x = number of friends who originally agreed to share the cost.
y = cost per friend.
total cost = 525.
x * y = 525
when 6 friends join, x becomes x + 6
when the price is dropped by 10 dollars, y becomes y - 10
total cost is still 525.
(x + 6) * (y - 10) = 525
you have two equations that need to be solved simultaneouly.
they are:
x * y = 525
(x + 6) * (y - 10) = 525
simplify the second equation to get:
x * y - 10 * x + 6 * y - 60 = 525
from the first equation, solve for x to get x = 525 / y
in the second equation, replace x with 525 / y to get:
525 / y * y - 10 * 525 / y + 6 * y - 60 = 525
simplify to get:
525 - 5250 / y + 6 * y - 60 = 525
multiply both sides of the equation by y to get:
525 * y - 5250 + 6 * y^2 - 60 * y = 525 * y
the 525 * y in both sides of the equaton cancels out and you get:
- 5250 + 6 * y^2 - 60 * y = 0
reorder the terms in descending order of degree to get:
6 * y^2 - 60 * y - 5250 = 0
divide both sides of the equation by 6 to get:
y^2 - 10 * y - 875 = 0
factor this quadratic equation to get:
y = -25 or y = 35.
y has to be positive, so y = 35.
y is the original cost to each friend.
since x * y = 525, then x = 525 / y = 525 / 35 = 15.
the original number of friends was 15 and they each would have to pay 35 dollars each.
6 friends joined for a total of 21 friends.
525 / 21 = 25.
the cost of 35 dollars for each friend dropped from 35 dollars per friend to 25 dollars per friend.
this confirms the solution is correct.
Answer by VFBundy(438)  (Show Source):
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