Math Worksheets

Archive for August, 2011

Question: I need help on math problems for homework!?

I need help with the following questions on my math worksheet.
They are kind of “brain-teaser” questions and I can’t figure them out.

3. A certain product is sold as either powder or a liquid. A survey reveals that 1/3 of the consumers interviewed do not use powder, 2/7 do not use the liquid, 427 use both liquid and powder and 1/5 do not use the product at all. How many consumers were interviewed?

4. Find the one’s digit of 1998^1999 – 1999^1998 (explanation please!)

6. From an 8.5″ by 11″ sheet of paper, x” by x” squares are cut from 2 corners and x” by 5.5″ rectangles from the other 2 corners. The paper is then folded to form a box with a lid. Express the volume of the box in terms of x.

Any explanations will be greatly appreciated. Thank you so much for your time!

Answer: 1).
Let the number of consumers interviewed be x.
(1/3)x + (2/7)x = (13/21)x do not use either powder or liquid of the product.
(1/5)x do not use the product at all.
Number of people using both liquid and powder are
[1 - (13/21 + 1/5)]x = [1 - (86/105)]x = (19/105)x = 427
x = 427*105/19 = 2360

2).
1998^1999 – 1999^1998
= 1998^(1998 + 1) – (1998 + 1)^1998
= 1998^1998 + 1998^1 – (1998^1998 + 1^1998)
= 1998 – 1 = 1997
The one’s digit of 1998^1999 – 1999^1998 is therefore 7

3).
Given an 8.5″ by 11″ sheet of paper:
x” by x” squares are cut from 2 corners and
x” by 5.5″ rectangles are cut from the other 2 corners.
The paper is then folded to form a box with a lid.
The dimensions of the box so formed is
x’ by x” by 5.5″
The volume of the box = 5.5 x^2 cubic inches.