A family will rent a picnic shelter for $200 for a reunion. The cost of the shelter will be distributed equally among the people who plan to attend. The current cost per person will decrease by $1 if 10 more people plan to attend the reunion. How many people are currently planning to attend the reunion?
F. 10
G. 20
H. 40
J. 50
K. 63
let x be the number of people who plan to attend right now.
cost of attending = price divided by number of people attending
the present cost of attending = 200/x
the cost of attending if 10 more people come = 200/(x+10)
since the cost of attending reduces by 1 if 10 more people attend,
200/(x+10) = (200/x) - 1
solving for x
200/(x+10) = (200-x)/x (common denominator)
200x= (200-x)(x+10) (cross multiply)
200x = 200x +2000 - x^2 - 10x ( multiply it out)
0 = -x^2 -10x +2000 (subtract 200x from both sides and rearrange)
(x+50) ( -x+40) = 0 (factorize)
two solutions :
x+50 = 0
x= -50
or
-x +40 = 0
x = 40
since the number of people cant be negative, the answer is 40 or option H.
Now for the dummies like me who don’t understand rocket science.
Guess and check!
H) 40.
$200 ÷ 40 = $5.
$200 ÷ 50 = $4.
That works!