A person has 14000 invested in stock A and stock B. A currently sells for $40 a share and stock B sells for 60 a share. If stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000. How many shares of each stock does he own?

Answer:He own 200 shares of stock A and 100 shares of stock B.Step-by-step explanation:Let x be the number of shares of stock A and y be the number of shares of stock B.Current value of a share of stock A = $40Current value of a share of stock B = $60A person has 14000 invested in stock A and stock B.[tex]40x+60y=14000[/tex]Divide both sides by 20.[tex]2x+3y=700[/tex]            .... (1)Stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000.New value of a share of stock A = $40 + (50% of 40)= $40 + $20 = $60New value of a share of stock B = $60 × 2 = $120[tex]60x+120y=24000[/tex]Divide both sides by 60.[tex]x+2y=400[/tex]            .... (2)Solve equation (1) and (2) by elimination method.Multiply 2 on both sides in equation (2).[tex]2x+4y=800[/tex]       .... (3)Subtract equation (3) from equation (1).[tex]2x+3y-2x-4y=700-800[/tex][tex]-y=-100[/tex][tex]y=100[/tex]The value of y is 100.Substitute y=100 in equation (1).[tex]2x+3(100)=700[/tex][tex]2x+300=700[/tex]Subtract 300 from both sides.[tex]2x=700-300[/tex][tex]2x=400[/tex]Divide both sides by 2.[tex]x=200[/tex]The value of x is 200.Therefore he own 200 shares of stock A and 100 shares of stock B.