Tim had some cranberry biscuits and banana biscuits. ³₄ of the number of cranberry biscuits was equal to ¹₃ of the number of banana biscuits. After Tim made -3 more cranberry biscuits, the number of cranberry biscuits was ¹₃ of the number of banana biscuits. How many biscuits did he have altogether in the end?
Make the numerators the same. LCM of 3 and 1 is 3.

34 of cranberry biscuits = 1x33x3 of banana biscuits

³₄ of cranberry biscuits = ³₉ of banana biscuits

	Cranberry biscuits	Banana biscuits	Total
Before	4 u	9 u
Change	+ -3
After	1x3 = 3 u	3x3 = 9 u	12 u

The number of banana biscuits remains unchanged.  Make the number of banana biscuits the same.  LCM of 3 and 9 is 9.

Number of more cranberry biscuits made
= 3 u - 4 u
= -1 u

-1 u = -3

1 u = -3 ÷ -1 = 3

Number of biscuits that Tim had in the end
= 3 u + 9 u
= 12 u
= 12 x 3
= 36

Answer(s): 36