Question 1172822
.
During a football season one team scored 23 goals more than the other. Between them they scored 135 goals. 
How many goals did each team score
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            There are several ways to solve this and similar problems.



<U>One way to solve</U> &nbsp;&nbsp;&nbsp;&nbsp;for very beginning students


<pre>
    one team scores + team scores = 135   scores, in all.

        x           +  (x - 23)   = 135

       2x                         = 135 + 23 = 158

        x                         = 158/2 = 79


    <U>ANSWER</U>.  One tewm scored 79;  the other team scored 79-23 = 56.


    <U>CHECK</U>.   79 + 56 = 135 scores, total.   ! Correct !
</pre>


<U>ANOTHER way to solve</U> &nbsp;&nbsp;&nbsp;&nbsp;for more mature students


<pre>
You write the system of two equations


    x + y = 135      (1)   (x = one tem scores;  y = the other team scores)

    x - y =  23      (2)


and add equations.


You get then  2x = 135+23 = 158;  x = 158/2 = 79.


As the last step, from equation (1)  y = 135 - 79 = 56.


You get the same answer.
</pre>


<U>Third way</U>  &nbsp;&nbsp;&nbsp;&nbsp;for mature experts, who solved such problems tens and hundreds of times


<pre>
They know that one team get half the sum  of given numbers  {{{(135+23)/2}}} = 79,

         while the other team get half the difference of given numbers  {{{(135-23)/2}}} = 56.
</pre>

Solved, explained and completed.



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