A word problem on percentages

Percentages are used to express how large one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of $ 0.15 on a price of $ 2.50 is an increase by a fraction of 0.15 / 2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase.

Let's see a word problem on it.

Question:-

A waitress earn an average tip of 12% of the cost of the food she serves.If she serves $ 375 worth of food in one evening ,how much money in tips will she earn on average.

Answer:-

Waitress serves food worth=$375

She earns a tip=12%

     So.
           12% of $375


       12
      ----- * 375
       100

      12*375
     ---------
       375

       4500
   =  -------
        100

   =$45

 So the waitress earn a tip of $45.

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problem on solving linear equations

Topic:-linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state.

Question:-

solve |5b-3| = |3b+7|

Answer:-
This math help is from linear equations.

This is of the form |a|=|b|

which implies a = +b
        or a = -b

Using this we get

    5b-3=+(3b+7)

    5b-3=-(3b+7)

5b-3 =+(3b+7)|  5b-3 =-(3b+7)
            |
5b-3 = 3b+7 | 5b-3 = -3b-7
            |
bring 3b    |
left        | bring 3b left
hand side   | hand side
            |
5b-3b=7+3   | 5b+3b= -7+3
            |
2b = 10     | 8b= -4
            |
b = 5       | b = -4/8
            |
            | b = -1/2

So b= 5 or -1/2 is the answer

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