Math

Word Problem Woes

Tips for Solving

       When defining your variables look for the word "than" or "as." These are comparison words.  Whatever comes after "than" or "as" assign the single x.

Example:  Charlie has 2 more nickels than dimes. Here you have two unknowns, the number of nickels and the number of dimes.   Dimes comes after the word than so dimes =x.

Re-read the sentence and define the other unknown.  Let nickels equal 2+x.

       The second equation is usually your equation sentence.

       The verb of the equation sentence is your equal sign.  That will separate the words for your left and right side.

       Usually the first sentence defines the variable and the second one is the equation sentence.  It can be backwards though.

       Twice means two times  2(          ).  Use your parentheses.

       Use tables for distance, age, work and mixture problems.  In a table you multiply across and add down the last column for your equation.

       For work problems the rate is the reciprocal of the entire time to do the job.

Example:  If John takes 3 hours to mow the lawn, then John's rate is 1/3.  It is the amount of the job he can finish in one unit of time. 

       "Less" means to subtract in the same order.  6 less the number of socks is 6-x

"Less than" means to subtract in the reverse order.  6 less than the number of socks is x-6.

”Is less than" is the symbol <.  The number of socks is less than 6.  x<6

       If you have ratio problems, say 3:4 define your variables as 3x and 4x.  If you have 2:3:7:  Then define the variables as 2x, 3x, and 7x.

       Percent problems use   Start with your percent over 100 then fill in the denominator for what ever comes after the word of.  Cross multiply and solve.  The word what is your x. 

Example:  8 % of what number is 57. 

       Consecutive numbers are set up as n, n+1, n+2, n+3, etc.

       Consecutive odd numbers are set up as n, n+2, n+4, n+6, etc. To get from one odd to the next odd you add 2.

       Consecutive even numbers are set up as n, n+2, n+4, n+6, etc. To get from one even to the next even you add 2.

       Two digit number                                                        Three digit number

x is ten's place                                                             x is hundred's place

y is one's place                                                             y is ten's place

The number is 10x+y                                  z is one's place

The number reversed is y+10x                 The number is 100x+10y+z

                                                                                        The number reversed is 100z+10y +x

       Coin Problems.

If x is the number of nickels

Y is the number of dimes

Value of the nickels is 5x

Value of the dimes is 10y.

       Distance

Arrows are end to end then you add the distances and set equal to the total distance apart.

If the arrows are parallel  such as a return trip, then you set these two distances equal to each other.

       Variation

o        Direct variation is y=kx.  The graph will go through the origin.

o        Inverse variation is y =k/x   or xy=k

Your first set of data will allow you to solve for k.

Words and what they mean!