Expert: Stephen King - 10/23/2004

Question
I have some problems there kinda like word problems and im not understanding them you have to solve each of the following step by step using the 5 step method and could you write them out step by step please.

1. One-third of anumber is 5 less than half of the same number.

2. The sum of a number and its reciprocal is 10 over 3. What is the number?

3. An investment of $1500 paid interest of $45 during a certain period. How much interest would an investment of $2000 invested at the same rate for the same length of time pay.

4. In baseball a players batting average is the ratio of hits to the number of times he or she has batted. Thou, if the player has an average of .300 it means he or she got 300 hits in 1000 at bats. In order to have an average of .300 how many hits would the batter have to get in 400 times at bat.

If you could please help me with these 4 problems I would appreciate it.

Answer
Hello Jamie.

I have no idea what the 5-step method is.  But I can solve all of these problems for you:

1.  1/3n=1/2n-5  (translate the words to math)
(1/6)n=5
n=30

2.  n+(1/n)=(10/3)
Use the quadratic formula to solve for n:
n=3  or  n=1/3
Both will work (Why?)

3.  A=P(1+ni), where A=amount after interest, P=principal amount, n=time interest accrues, and i=rate of interest.

1545=1500(1+.5i) (just pick a time since it wasn't specific)
Solve for i:
1545/1500=1+.5i
103/100=1+.5i
3/100=.5i
6/100=i
So i=6%

Now find A using 2000 for P:
A=2000(1+.5(.06))
A=2060
So the interest would be $60.

4.  300/1000=x/400
See why this works?
300(400)=1000x
120000=1000x
120=x
So the batter would have to hit 120 times.

Steve