Question 983046


Let &nbsp;<B>a</B></B>&nbsp; be the amount that Al spent &nbsp;(in Php);

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>b</B>&nbsp; be the amount that Bill spent &nbsp;(in Php), &nbsp;and 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>c</B>&nbsp; be the amount that Carl spent &nbsp;(in Php). 


Then you have &nbsp;3&nbsp; equations in &nbsp;3&nbsp; unknowns:


a + b &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 1200, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b + c = 1800, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)

a + &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c = 1000. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(3)


Add all three equations &nbsp;(which means "add their left sides and add their right sides"). &nbsp;You will get 


2*(a + b + c) = 1200 + 1800 + 1000 = 4000, &nbsp;&nbsp;&nbsp;&nbsp;or


a + b + c = 2000. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(4)



Now, &nbsp;distract the equation &nbsp;(1)&nbsp; from &nbsp;(4). &nbsp;You will get


c = 2000 - 1200 = 800. &nbsp;&nbsp;Hence, &nbsp;Carl spent &nbsp;800 Php.



Next, &nbsp;distract the equation &nbsp;(2)&nbsp; from &nbsp;(4). &nbsp;You will get


a = 2000 - 1800 = 200. &nbsp;&nbsp;Hence, &nbsp;Al spent &nbsp;200 Php.



Finally, &nbsp;distract the equation &nbsp;(3)&nbsp; from &nbsp;(4). &nbsp;You will get


b = 2000 - 1000 = 1000. &nbsp;&nbsp;Hence, &nbsp;Bill spent &nbsp;1000 Php.



<B>Answer</B>. &nbsp;Al spent &nbsp;200 Php, &nbsp;Bill spent &nbsp;1000 Php, and &nbsp;Carl spent &nbsp;800 Php.



For more similar problems see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/The-trick-to-solve-some-word-problems-with-three-and-more-unknowns.lesson>The tricks to solve some word problems with three and more unknowns using mental math</A>&nbsp; in this site.