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Question 54940: JANE , THE SALES REPRESENTATIVE OF DT.COM EQUIPMENT LTD IN 3 DAYS OF TRIAL SALES IN WESTERN REGION OF THE COUNTRY SOLd 2 P'CS AND 3 CD PLAYERS AND 4 TV'S ON THE FIRST DAY;3 PC'S AND ONE CD PLAYER , AND 2 TV'S ON THe SECOND DAY ; 5 PC'S AND 2 C'D PLAYERS , AND ONE TV ON THE THIRD DAY . HE RECEIVED A TOTAL ( 000KSH) OF 250,190, AND 280 ON THE FIRST, SECOND AND THIRD DAY RESPECTIVELY . WHEN HE WAS HANING OVER THE MONEY TO THE ACCOUNTANT HE WAS UNABLE TO ANSWER OF HOW HE SOLD A UNIT OF EACH ITEM .
QUESTION :
ASSIST THE ACCOUNTANT WHO ACTUALLY REQUIRED THESE FIGURS FOR PROPER RECORD KEEPING
Answer by foleysdad(7)   (Show Source):
You can put this solution on YOUR website! This problem has three variables and therefore requires three equations. The variables are the price of PCs which we will call P, the price of CD players which we will call C and the price of TVs which we will call T.
The equations are the following taken directly from the text.
2P+3C+4T=250
3P+1C+2T=190
5P+2C+1T=280
You must solve two equations for the other two, Since one of the variables equals one in two of the equations, let's solve for those.
The first equation is
3P+1C+2T=190 subtract 3P from both sides
1C+2T=190-3P subtract 2T from both sides
1C=190-3P-2T Done
The second equation is
5P+2C+1T=280 subtract 5P from both sides
2C+1T=280-5P subtract 2C from both sides
1T=280=5P-2C Done
Put the first equation into the second.
T=280-2C-5P Put in first equation answer
T=280-2(190-2T-3P)-5P Multiply out
T=280-380+4T+6P-5P Simplify
T=-100+4T+1P add 100 to both sides
T+100=4T+1P subtract 4T to both sides
T-4T+100=1P simplify
-3T+100=P
Put this answer into the first equation.
C=190-2T-3P substitute
C=190-2T-3(100-3T) Mulitply
C=190-2T-300+9T simplify
C=-110+7T
Put these two answers into an original equation.
2P+3C+4T=250 Original equation now insert results
2(-3T+100)+3(-110+7T)+4T=250 Multiply out
-6T+200-330-21T+4T=250 add 330 to both sides
-6T+200-21T+4T=250+330 subtrcat 200 from both sides
-6T-21T+4T=380 simiplify
19T=380 divide by 19
T=20 Done
Plug T into equations
P=100-3T
P=100-3(20)
P=100-60
P=40
C=-110+7T
C=-110+7(20)
C=-110+140
C=30
Now Check you answers:
2(40)+3(30)+4(20)=250
80+90+80=250
3(40)+1(30)+2(20)=190
120+30+40=190
5(40)+2(30)+1(20)=280
200+60+20=280
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