cold mixes a powdered sports drink with cold water ls To kee

cold mixes a powdered sports drink with cold water. ls. To keep his baseball team hydrated, Daniel as used 16 scoops of powder mix he add, given that each scoop added 2 quarts of water, how many gallons of water should th) awuf 15 6 gallons waler (16. A age wants to build a community center that is to cost 1.2 million dollars. than Cost per resident is increased discovered that there are 225 residents when planning began 2 years ago. What is the revised cost per resident?

Solution

Only one question can be answered at a time. Hence it is Q 16 is being answered.

Let $ x be the cost per resident, originally. Also let the number of residents considered earlier be n. Now the revised cost is $ x+3 per resident and the number of residents being considered is n-225. Thus

nx= 1200000= (n-225)(x+3), as the total cost remains 1200000.

From nx= 1200000, n= 1200000/x; From (n-225)(x+3)= 1200000, it is nx-225x +3n-675= 1200000. In this equation substitute nx= 1200000 and n= 1200000/x, to get

1200000-225x +3 (1200000/x) -675= 1200000

Or, -225x + 3600000/x -675=0, Now multiply all terms by x,

-225x² -675x +3600000=0

225x² +675x- 3600000=0, Now divide all terms by 225,

x² +3x -16000=0. , Now this quadratic can be factorised as follows:

x² +128x -125x -16000=0

x(x+128)-125(x+128)=0

(x+128)(x -125)=0, Hence x= -128 or 125. Reject the negative value, hence x= 125

$125 was thus the original cost per resident. The revised cost is therefore $128.... Answer

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