[infiniti]

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 :cool: