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On the tray, they had apricot and plum cakes in a ratio of 3:2. After eating three apricot pies, the chance of taking out a plum and apricot was the same. How many cakes were there together on the tray at the beginning?

Correct answer:

x =  15

Step-by-step explanation:

a:b=3:2  2a=3b a3=b  2 a=3 b a3=b  2a3b=0 ab=3  Row212 Row1Row2 2a3b=0 0.5b=3  b=30.5=6 a=0+3b2=0+3 62=9  a=9 b=6  x=a+b=9+6=15a:b = 3:2 \ \\ \ \\ 2a = 3b \ \\ a-3 = b \ \\ \ \\ 2 \cdot \ a = 3 \cdot \ b \ \\ a-3 = b \ \\ \ \\ 2a-3b = 0 \ \\ a-b = 3 \ \\ \ \\ Row 2 - \dfrac{ 1 }{ 2 } \cdot \ Row 1 → Row 2 \ \\ 2a-3b = 0 \ \\ 0.5b = 3 \ \\ \ \\ b = \dfrac{ 3 }{ 0.5 } = 6 \ \\ a = \dfrac{ 0+3b }{ 2 } = \dfrac{ 0+3 \cdot \ 6 }{ 2 } = 9 \ \\ \ \\ a = 9 \ \\ b = 6 \ \\ \ \\ x = a+b = 9+6 = 15



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