Hi alll-

I have two homework problems that I need help with:

1. How many liters of pure water should be evaporated from 7.5 liters of a 15% acid solution so that the solution that remains is a 20% acid solutions.

2. The number N of guests that arrive at a mall food court each hour can be approximated by N = -12x(square) + 110x + 35, where x is the number of hours after 11:00 am. At what times, to the nearest minute, are 200 guests per hour arriving at the food court?

Thanks for helping in advance.

CroCivic91

1. You currently have 7.5 liters of mixture. In that mixture there is 15% acid. That means that there is 7.5*0.15=1.125 liters of acid. Now you want to have a mixture of 20% acid, that means that X*0.2=1.125 where X is the amount of mixture in which 1.125 liters of acid would make 20%. From that, we get that X = 5.625 liters. Difference between those two is 7.5 - 5.625 = 1.875. That means that 1.875 liters of water should evaporate to get a 20% acid mixture.

infiniti

That makes sense. Thanks.

I hate word problems.

shanus

2. The question isn't as hard as it looks...its simply a quadratic formula.
N, being the number of guests that arrive per hour = 200,

200 = -12x^2 + 110x + 35 rearranged this gives:
-12x^2 + 110x -165 = 0
Two x values that this is true for are 7.28 and 1.88, these are the number of hours past 11:00am the number of guests per hour is 200.
Therefore the times at N = 200 are 6:17pm and 12:53pm