# One hundred bushels of corn are to be divided among 100 persons. men get 3 bushels each, women 2 and children 1/2. how many men, women and children are present?

Friday, October 1st, 2010

### Solution:

1. Let m = the number of men (an integer)
2. Let w = the number of women (an integer)
3. Let c = the number of children (an integer)
4. Number of bushels = 3m+2w+.5c = 100
5. Number of people = m+w+c=100
6. 0<m<100
7. 0<w<100
8. 0<c<100

If we assume that there are 10 children, then we can solve for two equations and two unknowns:

1. 3m+2w+5 = 100
2. m+w+10=100

We can solve this by subtracting two times the second equation from the first equation:

1. 3m+2w+5 = 100
2. 2m+2w+20=200 (this is two times the second equation shown above)
3. m          – 15 = -100 (this is the result of subtracting two times the second equation from the first equation)
4. m = -85
5. w=100-10- (-85) = 175

The problem with this result is that the values for m and w are outside the allowable range, so clearly the assumption that there are 10 children is wrong. Let’s try increasing the number of children to 80 and see how that impacts the result from m:

1. 3m+2w+40 = 100
2. 2m+2w+160=200
3. m          -125 = -100
4. m                 =  25
5. w = 100-80-25=-5

Here, the result for m is within the range, but the value for w is outside the range. Let’s try reducing the number of children to 70:

1. 3m+2w+35 = 100
2. 2m+2w+140=200
3. m          -105 = -100
4. m                    =    5
5. w = 100-70-5= 25

Now we have a solution that makes sense (m=5, w=25, c=70). However, there may be other answers that work, so let’s try increasing the number of students to 72 and see what happens:

1. 3m+2w+36 = 100
2. 2m+2w+142=200
3. m          -106 = -100
4. m                    =    6
5. w = 100-72-6= 22

This solution also makes sense (m=6, w=22, c=72). Clearly, there can be several correct solutions to this question.

# What is 43 over 100 as a decimal.

Friday, October 1st, 2010

### Solution:

The answer is forty three hundredths, which is written as 0.43.

# Suppose a Word is a String of 8 letters of the Alphabet with Repeated Letters Allowed: (5 points, 1 point each) Show all work. Do not Answer with just a Number. 1. How many words are there? 2. How many words end with the letter N? 3. How many words begin with R and end with N? 4. How many words start with A or B? 5. How many words begin with A or end with B

Friday, October 1st, 2010

### Solution:

1. If you have 26 choices for each letter in a word, then there are 26 such one-letter words, 262 two-letter words, 263 three-letter words, etc. There would be 268 eight-letter words.
2. There would be 267 eight-letter words that end with the letter N, which is the same as the number of 7 letter words (just add “N” to the end of each seven-letter word.
3. There would be 266 eight-letter words that begin with R and end with N (just add R to the front and N to the end of all six-letter words.
4. There would be 2*267 eight-letter words that begin with an A or B (add A to the beginning of every seven-letter word, then add B to the beginning of every seven-letter word).
5. There would be 2*267 eight-letter words that begin with A or end with B (add A to the beginning of every seven-letter word, then add B to the end of every 7 letter word).

# Complete These Ordered Pairs: (0, ) (2, ) (-1, ) y=3x-1 (-1, ) (0, ) (1, ) 2x+y=3 (0, ) (-1, ) (1, ) y=2x+1

Friday, October 1st, 2010

### Solution:

Each ordered paid represents x and y: (x,y)

To calculate y, you can plug in x.

If y=3x-1, then the given values of x will result in the pairs (0,-1) (2,5) (-1,-4).

If y=3-2x, then the given values of x will result in the pairs (-1,5) (0,3) (1,1).

If y=2x+1, then the given values of x will result in the pairs (0,1) (-1,-1) (1,3).

# In trapezoid ABCD the median MN cuts diagonals AC =D at p and q repectively, BC=12, and AD=20 Determine PQ please explain your steps. i know the median is 16 and I know the correct answer is 4, I know there is a formula but we have not proved it.

Friday, July 23rd, 2010

### Solution:

First, let’s draw the trapezoid so that we can visualize the problem. We have not drawn the trapezoid exactly to scale, but this should be accurate enough for our purposes:

Now, we know that MN = 16 because the median equals the average of the top and bottom of the trapezoid

We also know that the distance of Mp = 6, because it just be half the length of BC (the sides of triangle AMp are half the size of the sides of triangle ABC because the triangles are similar and we know that AM is half the length of AB since MN is the median).Similarly,the length of qN = 6.

Now it’s easy to solve for pq:

1. Mp + pq + qN = MN = 16
2. 6 + pq + 6 = 16
3. pq = 4