Two grandmothers

Two grandmothers went to sell eggs at the market, and they had 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 answer:

a =  60
b =  40

Step-by-step explanation:

a+b=100 a c1 = b c2 a c2 = 15 b c1 = 6 + 2/3 = 320 = 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 (6 3+2)  3 (100a) (100a) 15=a2 (6 3+2) 25a29000a+450000=0 25=52 9000=233253 450000=243255 GCD(25,9000,450000)=52=25  a2360a+18000=0  p=1;q=360;r=18000 D=q24pr=36024118000=57600 D>0  a1,2=2pq±D=2360±57600 a1,2=2360±240 a1,2=180±120 a1=300 a2=60  0<a<100 a=a2=60  c1=(100a) (15/a)/a=(10060) (15/60)/60=610.1667  c2=15/a=15/60=41=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=320=6326.6667

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