Ethan's Responses in WyzAnt Answers

Let's consider a problem of adding apples and oranges.  If I have 3 apples and a friend gives you 2 more apples you have 3+2 = 5 apples.  Now let's say you have 3 apples and a friend gives you 4 oranges.  How many apples do you have?  You have 3 + 0 = 3 apples.  You cannot add apples and oranges together because they are two different things.  Now let's apply this to variables.  Let's say you have x and you want to add 3 more x.  You get 1x+3x = 4x.  You can just add the coefficients together because you are adding the same thing.  If the question was x+2y, these are different variables (adding apples and oranges) and cannot be simplified any further.

Now let's say I gave you an equation 3x +2y +6x + 10y, can you simplify?

You can write this as two equations by saying the positive and negative of the inside of the absolute value is equal to 15.  This will give 2y - 2 = 15 and -(2y-2) = 15.  For the first equation we add two to both sides to get 2y - 2 +2 = 15 + 2.  This givese you 2y = 17.  We then divide both sides by two to get 2y/2 = 17/2 which gives y = 8.5.  Now let's work with -(2y-2) = 15.  We use the distributive property to get rid of the parenthesis and distribute the negative throughout.  We get -2y + 2  = 15.  Subtract 2 from both sides:

-2y +2 - 2 = 15 - 2 = 13.  Now we have -2y = 13.  Now divide both sides by -2 and we get -2y/-2y = 13/-2 which gives y = -6.5.

The last step is to check your answers by plugging in your values you find for y into the original equation.  This gives |2*8.5 - 2| = 15 is true and |2*-6.5 - 2| = 15 is also true.  Your answers are correct!

|x| = 0 means that x has to be equal to either the negative or positive value.  This is called the absolute value.  0 is not negative or positive and therefore the equation has one solution.  The solution is x = 0.

First let's get the variable y all onto one side.  We do this by subtracting y from each side to get

3y - y = y - y + 10.  This gives us 2y = 10.  Then we divide each side by 2 and get 2y/2 = 10/2 and get 

y = 5.  We then check our answer by substituting 5 into the original equation.  3*5 = 5 + 10 = 15.

9)  Percent change is the amount of change with respect to the old price.  The equation is % change =

100*(new - old)/old = 100*(new/old - 1).  We then plug in 70 for old and 49 for new and get 100*(49/70-1) = -30.  The perecent change is -30%.

10.  We have the original price of $110.  We get 30% off of the original price.  So we get $110 minus the 30% of the 110 = 110 - 110*30% = 110 - 110*.3 = 77.

11.  You earn 22% of the $4,000 dollars.  A percentage is a fraction.  So you will not get the FULL $4,000 you will get only a fraction or percentage of it.  In this case it is 22%.  Whenever you see the word "of" in a percentage question like this, think multiply.  We take 4,000*22%  = 4,000*.22 = 880.  You get $880 of commission this month.

12.  This is a mark UP price not a mark DOWN price.  So we want to add the 30% to the original price.  65+65*.3 = 84.5.  Note:  We can factor out a 65 in that equation to get 65+65*.3 = 65(1+.3) = 65*1.3 = 84.5.  When marking up we can multiply the original price by (1+ % markup) because we get 100% of the original plus 30% of the original.

13.  The best way to approach this is to convert all of these to either fractions or percentages.  I will choose percentages.  We only need to get 5/4 and 1.3 to a percentage.  They are 5/4 = 125% and 1.3 = 130%.  Now just ordering from smallest to largest you get (.345%, 4.6%, 13%, 120%, 125%, 130%)