Posted on

# Homework help 6-46

## Math Homework Help

You have been asked to organize the school band so it can march in this year’s community parade. The band can have from 60 – 85 people, and will march in rows and columns. Each row has the same number of people in it. You cannot have rows or columns with more than 9 people.

How can you arrange the people in the band?

A. Create all the REASONABLE arrays you can to fit 60 to 85 people in the band. This is different from class when we made looked at all possibilities for the bus problem. It would not make sense for 60 people to walk single file, an array of 60 by 1.
B. Write the fact family for each of your arrays. A fact family is the multiplication and the division number sentence. For example, 1 x 60 = 60 and 60/1 = 60 is in the same fact family.
C. Explain how you know you found all the possible arrays in Part A. Yes, use WORDS to explain what you did.
D. Choose 1 array. Explain how the fact family describes it. Again, use WORDS to explain what you did.

Drake’s Boy Scots troop sold 235 boxes of hot chocolate (\$7.00 each) and 256 tins of popcorn (\$8.00 each). Teresa’s Girl Guide unit sold 95 carry cartons of cookies. Each carry carton contains 12 boxes of cookies (\$4.00 each box).

A. How much money did the Boy Scouts raise? 235 x \$7.00 PLUS 256 x \$8.00.

B. How much money did the Girl Guides raise? 12 x \$4.00. THEN that answer x 95.

C. Who sold more? How much more was raised?

D. Each group had a goal to raise a total of about \$10,000. How many more items would the Boy Scouts need to sell to reach the goal?

E. How many more items would the Girl Guides have to raise to reach the goal?

## Quadratic Equations: Finding three consecutive positive integers given sum of squares

1. Three consecutive positive integers are such that the sum of the squares of the first two and the product of the other two is 46. Find the numbers. Variables: x. Three numbers: (x), (x + 1), (x + 2)

2. (I think, although I’m not sure.) x 2 + (x + 1) 2 + (x + 1)(x + 2) = 46

3.
x 2 + (x + 1) 2 + (x + 1)(x + 2) = 46
⇒ x 2 + x 2 + 1 + 2x + x 2 + 3x + 2 = 46
⇒ 3x 2 + 5x + 3 = 46
⇒ 3x 2 + 5x – 43 = 0
⇒ x 2 + ( 5 /3)x – 43 /3 = 0 /3
⇒ x 2 + (2)( 5 /6)(x) + ( 5 /3) 2 – ( 5 /3) 2 – 43 /3 = 0
⇒ (x + 5 /6) 2 = 43 /3 + 25 /36
⇒ (x + 5 /6) 2 = 516 + 25 /36 = 541 /36

Now this means x + 5 /6 is NOT a perfect square. And that means the three consecutive positive integers will also not be positive integers.