Mathematics Exeter Problems 1

This may be pointless to most of you but this is for some of my fellow classmates who need help on the math exeter problems. But you can still do this if you want to just learn some math! But also, please correct me if I'm wrong.

1. Woolworth's had a going-out-of-business sale. The price of a telephone before the sale was $39.98. What was the price of the telephone after a 30% discount? IF the sale price of the same telephone had been $23.99, what would the (%) discount have been?

First, let's work on the first half of the problem: To find a discount you convert the percentage to a decimal or fraction; So the equation equals $39.98 x .30= 11.994----> 11.99

But now, don't forget to subtract this from the original price. This is only the discount! so 39.98-11.99= $27.99

Another simpler way to do this is to use $39.98 x (1- .30)= $27.99

The main formula for the second part is (original-sale)÷(original)= percent change
So, (39.98-23.99) ÷ (39.98)= %
15.99÷39.98= %
%= .40------> 40%

2. Pick any number. Add 4 to it and then double your answer. Now subtract 6 from that result and divide your new answer by 2. Write down your answer. Repeat these steps with another number. Continue with a few more numbers, comparing your final answer with your original number. Is there a pattern to your answers?

Well to test you always want to use easy numbers like 1 or 0. So.....

((1+4) x 2 -6) ÷ 2= 2

Now,

((0+4)x 2 -6) ÷ 2= 1

As you see, both answers increase the value by 1. So conclusion, the steps bring your original answer up by one. If you thing about it, its 4 x 2, which is 8, then -6, which is 2, then ÷ 2, which is 1.

3. Using the four intergers 2, 3, 6 and 8 once each -- in any order-- and three arithmetic operations selected from among addiction, subtraction, multiplication, and division, write expressions whose values are the target numbers given below. you will probably need to use parentheses. For example, to hit the target 90, you could write 90 = (3+6) x (8+2).

(a) 3 (B)24 (c) 36 (D) 30


(a) 3= (8-6)+(3-2)

(b) 24= (3 x 6) + (8-2)

(c) 36= (2x6)+(3 x 8)

(D) 30= ((8÷2) + 6 ) x 3

4. When describing the growth of a population, the passage of time is sometimes described in generations, a generation being about 30 yrs. One generation ago, you had two ancestors (your parents). Two generations ago, you had four ancestors (your grand-parents). Ninety yrs ago, you had eight ancestors (your great-grandparents). How many ancestors did you have 300 years ago? 900 years ago? Do your answers make sense?

Generation= g

1g= 2
2g= 4
3g= 8 <-----Notice that each generation is two times more than the one before 4g= 16 5g= 32 Also, notice that the generation number is the exponent of 2 to the # of ancestors. So the second generation corresponds to 2<sup>2.

Therefore, 300 yrs is equal to 10 generations. 2 to the power of 10 = 1024.

So after 300 yrs, you have approximately 1024 ancestors

For the second solution, 900 yrs is 30 generations. So the # of ancestors will be 2 to the power of 30. It is extremely tedious to do all that multiplication so an easy way to do is split it into parts.</sup>

2³⁰⁼ 2^{10 x} 2^{10 x} 2<sup>10

So, the answer turns out to be 1,135,178,924 ancestors. I know thats alot. Please correct me if it runs out wrong.</sup>