Beginning 6334

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 = 3:2b
a-3 = b
x = a+b

a = 3:2·b
a-3 = b
x = a+b

a-1.5b = 0
a-b = 3
a+b-x = 0

Row 2 - Row 1 → Row 2
a-1.5b = 0
0.5b = 3
a+b-x = 0

Row 3 - Row 1 → Row 3
a-1.5b = 0
0.5b = 3
2.5b-x = 0

Pivot: Row 2 ↔ Row 3
a-1.5b = 0
2.5b-x = 0
0.5b = 3

Row 3 - 0.5/2.5 · Row 2 → Row 3
a-1.5b = 0
2.5b-x = 0
0.2x = 3


x = 3/0.2 = 15
b = 0+x/2.5 = 0+15/2.5 = 6
a = 0+1.5b = 0+1.5 · 6 = 9

a = 9
b = 6
x = 15

Our linear equations calculator calculates it.



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