math project

math project
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  • hey mohanad, how much money did the pens and a4 notebooks cost you?
  • hey ali, i dont know how much exactly, but what i do know is that i boaght 4 pens and 7 a4 notebooks and it all cost me 47 dollars
  • ali goes to check with an other person
  • hey cousin ali m, how much money did the pens and a4 notebooks cost you?
  • what i remember is that i bought 5 pens and 3 a4 notebooks, it all cost me as i record about 30  dollars
  • after hearing both ali m and mohanad, ali decides to go back home and think of a way to figure out hoe much the pen cost and the a4 notebook 
  • if 4 pens and 7 a4 notebooks cost 47 dollars, and 3 a4 notebooks and 5 pens cost 30 dollars, then we can make an equation that can help me find how much a pen cost and how much an a4 notebook cost. plus we also just studied inverse matices which i can use in this sitiuation.
  • lets say pens are x  and y is a4 notebooks my equations would be: 3y+5x=30 and 7y+4x=47
  • but first we must multiply d and -b and -c and a toI 30 I                                                                                        I 40 I
  •  first i have to find IAI which equals to (5times7) mines (4times3) which equal 35-12= 23, now i use the equation used which is (1/ab-cd)multiplied by d then -b then -c then by a  
  • d=7, -b=-3, -c=-4, a=5. now lets multiply to B. which would equal to 7times30 - 3times47 and -4times 30 + 5times47. this all would equal 210-141 and -120+235. and finally all this would equal 69 and 115. 
  • what now?! oh.. i almost forgot i must multiply both numbers to 1/23 to find x and y
  • 1/23 times 69 = x and 1/23 times 115 =y.  which means that x= 3 and y=5. this means that a pen is 3 dollars and  an a4 notebook is 5 dollars. now that was easy. i never thought math is gonna actually help me in real life, i should pay more attention from now on. #thanks_mr_Hayyumsha 
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