Expert: Scott A Wilson - 2/9/2010

Question
1)a beaker contains 150cc of a solution  that is 30% acid. how much water must be evaporated so that the resulting solution will be 40%acid?

2)lois and clark leave their office to meet clients. lois leaves at 8am and travels at 35mph. clark leaves at 8:15am and travels at 40mph. they travel in opposite directions. when will they be 290 miles apart? (express all time in hours)

3)a certain amount of money is invested at 3.5%. $5000 more than three times that amount is invested at 4%. the total amount of interest earned in one year is $1440. how much is invested at each rate?

Answer
1) If there was 150 cc that was 30% acid, there was 150*0.3 = 45 liters of acid.
If this is suppose to be 40% of the solution, take 45 cc / 0.4 to get the entire solution.

Now 45/4 = 10.25, so 35/0.4 = 102.5.

That means since there can only be 102.5 left, he must boil off 150 - 102.5 = 47.5 liters.


2) Lois is travelling at 35 mph.  Dark travels at 40 mph.
That means the distance between them is increasing at 35+40 = 75 mph.
To achieve 290 miles, let m be miles and h be hours.  Take (290 m)/(75 m/h) and
get 10 miles short of 4 h.  Note that 10 m is 10/75 of an hour,
so the answer is 3 65/75 = 3 13/15 = 3 hours, 52 minutes.


3) Take the original amount as x and then the other amount will be x + 5000.
The total interest will be 0.035x + 0.04(x+5000) = 1440.
Multiplying out gives 0.035x + 0.04x + 200 = 1440.
That is the same as 0.075x = 1240.
That works out to be x = $15,633.33

Thus, $15,633.33 is invested in the 1st investment and
x+5000 = $20,633.67 is invested in the 2nd investment.