Chapter+3

=Constant Decrease...=

Problem:
After a flash flood, the level of water in the river was 54 inches above normal and dropping at a rate of 1.5 inches per hour. Let x equal the number of hours since the water started dropping and y equal the height, in inches, above normal of the lake. We can model this situation with the equation y = 54 - 1.5x. Graph this relationship.

Solution:
to find the lake level at various times and make a table. A table for 0, 1, 2, 3, 4, and 5 hours is shown below. Plot the ordered pairs in the table and look for patterns. You should see that the six points lie on the same line. Time in hours can be any non-negative real number, such as 1.75 or 1/2. This means that other points lie between the ones you have already plotted. So, draw the line through them for the domain x ≥ 0.

=Constant Increase...=

Problem:
Stephen collects coins. He begins with 25 coins and each week he is sent 10 new coins. After w weeks he will have 25 + 10w coins. Let t stand for the total number of coins he has at the end of w weeks. The size of Stephen's collection over these weeks can be described in number of ways. Three of them are shown below...

Solutions:
=Equation= =t=25 + 10w=

=Table= ==

=Graph= ==

Solving inequalities
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To clear fractions in an equation or inequality

 * 1) Choose a common multiple of all the denominators in the sentence.
 * 2) Multiply each side of the sentence with that number.

Clearing Decimals
Like fractions, decimals can be cleared from an equation to give a simpler equation with integer coefficients. A decimal can be thought of as a fraction whose denominator is a power of 10. For example, 0.4 can be written as 4/10, so the "denominator" of .4 is 10. Similarly, the "hidden denominator" of 9.38 (or 9 38/100) and 6.022 (or 6 22/1000) are 100 and 1000 respectively.

Explanation:
The equation involves two decimals: 5.85 and 2.7. Their "hidden denominators" are 100 and 10. Since 100 is divisible by both 100 and 10, multiply each side of the equation by 100. first you multiply by 100 and get 585n - 900 = 270 add 900 to each side and get 585n = 1170 then you divide each side by 585 and get n = 2.