Two grandmothers

Two grandmothers went to sell eggs at the market, and they had a total of 100. When they sold all the eggs, they made the same money. The first grandmother says to the second: "If I sold my eggs for your price, I would earn 15 crowns. " The other grandmother replies: "If I sold my eggs for your price, I would get 6 and 2/3 crowns. " How many eggs did each of the bucks have? Try to find the result without solving a complex quadratic equation.

Correct result:

a =  60
b =  40


a+b=100 a c1=b c2 a c2=15 b c1=6+2/3=203=6.666666   a c1=(100a) c2 a c2=15 (100a) c1=6+2/3  c2=15/a  a c1=(100a) (15/a) (100a) c1=6+2/3  c1=(100a) (15/a)/a  (100a) (100a) (15/a)/a=6+2/3  (100a) (100a) 15=a2 (6+2/3)  3(100a)(100a)15=a2(63+2)  3 (100a) (100a) 15=a2 (6 3+2) 25a29000a+450000=0  p=25;q=9000;r=450000 D=q24pr=90002425450000=36000000 D>0  a1,2=q±D2p=9000±3600000050 a1,2=9000±600050 a1,2=180±120 a1=300 a2=60   Factored form of the equation:  25(a300)(a60)=0  0<a<100 a=a2=60  c1=(100a) (15/a)/a=(10060) (15/60)/60=160.1667  c2=15/a=15/60=14=0.25

Our quadratic equation calculator calculates it.

b=100a=10060=40   Verifying Solution:   L1=a c1=60 0.1667=10 P1=b c2=40 0.25=10  L1=P1  L2=a c2=60 0.25=15 P2=b c1=40 0.1667=2036.6667

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